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2122693 | 10.1007/s00023-011-0104-5 | We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$
dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset
\Z^d$, are independent and their variances satisfy $\sigma_{xy}^2:=\E
\abs{H_{xy}}^2 = W^{-d} f((x - y)/W)$ for some probability density $f$. We
assume that the law of each matrix element $H_{xy}$ is symmetric and exhibits
subexponential decay. We prove that the time evolution of a quantum particle
subject to the Hamiltonian $H$ is diffusive on time scales $t\ll W^{d/3}$. We
also show that the localization length of the eigenvectors of $H$ is larger
than a factor $W^{d/6}$ times the band width $W$. All results are uniform in
the size $\abs{\Lambda}$ of the matrix. This extends our recent result
\cite{erdosknowles} to general band matrices. As another consequence of our
proof we show that, for a larger class of random matrices satisfying
$\sum_x\sigma_{xy}^2=1$ for all $y$, the largest eigenvalue of $H$ is bounded
with high probability by $2 + M^{-2/3 + \epsilon}$ for any $\epsilon > 0$,
where $M \deq 1 / (\max_{x,y} \sigma_{xy}^2)$.Comment: Corrected typos and some inaccuracies in appendix | Quantum Diffusion and Delocalization for Band Matrices with General
Distribution | quantum diffusion and delocalization for band matrices with general distribution | hermitian dimensions. indexed lambda variances satisfy sigma exhibits subexponential decay. diffusive localization eigenvectors lambda matrix. extends cite erdosknowles matrices. satisfying sigma eigenvalue epsilon epsilon sigma .comment corrected typos inaccuracies | non_dup | [] |
2181642 | 10.1007/s00023-011-0105-4 | A previously proposed algebra of asymptotic fields in quantum electrodynamics
is formulated as a net of algebras localized in regions which in general have
unbounded spacelike extension. Electromagnetic fields may be localized in
`symmetrical spacelike cones', but there are strong indications this is not
possible in the present model for charged fields, which have tails extending in
all space directions. Nevertheless, products of appropriately `dressed' fermion
fields (with compensating charges) yield bi-localized observables.Comment: 29 pages, accepted for publication in Annales Henri Poincar\' | Spacelike localization of long-range fields in a model of asymptotic
electrodynamics | spacelike localization of long-range fields in a model of asymptotic electrodynamics | asymptotic electrodynamics formulated algebras localized unbounded spacelike extension. electromagnetic localized symmetrical spacelike cones indications tails extending directions. nevertheless appropriately dressed fermion compensating charges localized pages publication annales henri poincar | non_dup | [] |
2158267 | 10.1007/s00023-011-0107-2 | In the present paper we study forward Quantum Markov Chains (QMC) defined on
a Cayley tree. Using the tree structure of graphs, we give a construction of
quantum Markov chains on a Cayley tree. By means of such constructions we prove
the existence of a phase transition for the XY-model on a Cayley tree of order
three in QMC scheme. By the phase transition we mean the existence of two now
quasi equivalent QMC for the given family of interaction operators
$\{K_{<x,y>}\}$.Comment: 34 pages, 1 figur | On Quantum Markov Chains on Cayley tree II: Phase transitions for the
associated chain with XY-model on the Cayley tree of order three | on quantum markov chains on cayley tree ii: phase transitions for the associated chain with xy-model on the cayley tree of order three | markov chains cayley tree. markov chains cayley tree. constructions cayley scheme. quasi .comment pages figur | non_dup | [] |
2113760 | 10.1007/s00023-011-0108-1 | We give pole free strips and estimates for resolvents of semiclassical
operators which, on the level of the classical flow, have normally hyperbolic
smooth trapped sets of codimension two in phase space. Such trapped sets are
structurally stable and our motivation comes partly from considering the wave
equation for Kerr black holes and their perturbations, whose trapped sets have
precisely this structure. We give applications including local smoothing
effects with epsilon derivative loss for the Schr\"odinger propagator as well
as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5
and Lemma 4.1; this now also corrects hypotheses, explicitly requiring
trapped set to be symplectic. Erratum follows references in this versio | Resolvent estimates for normally hyperbolic trapped sets | resolvent estimates for normally hyperbolic trapped sets | pole strips resolvents semiclassical normally hyperbolic trapped codimension space. trapped structurally motivation comes partly kerr holes perturbations trapped precisely structure. smoothing epsilon schr odinger propagator erratum correcting corrects hypotheses explicitly requiring trapped symplectic. erratum versio | non_dup | [] |
2120871 | 10.1007/s00023-011-0109-0 | Every set (finite or infinite) of quantum vectors (states) satisfies
generalized orthoarguesian equations ($n$OA). We consider two 3-dim
Kochen-Specker (KS) sets of vectors and show how each of them should be
represented by means of a Hasse diagram---a lattice, an algebra of subspaces of
a Hilbert space--that contains rays and planes determined by the vectors so as
to satisfy $n$OA. That also shows why they cannot be represented by a special
kind of Hasse diagram called a Greechie diagram, as has been erroneously done
in the literature. One of the KS sets (Peres') is an example of a lattice in
which 6OA pass and 7OA fails, and that closes an open question of whether the
7oa class of lattices properly contains the 6oa class. This result is important
because it provides additional evidence that our previously given proof of noa
=< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form
an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure | Kochen-Specker Sets and Generalized Orthoarguesian Equations | kochen-specker sets and generalized orthoarguesian equations | infinite satisfies orthoarguesian kochen specker hasse subspaces hilbert rays planes satisfy kind hasse greechie erroneously literature. peres pass fails closes lattices properly class. proper inclusion infinite successively stronger pages | non_dup | [] |
2148654 | 10.1007/s00023-011-0111-6 | We construct and discuss Hadamard states for both scalar and Dirac spinor
fields in a large class of spatially flat Friedmann-Robertson-Walker spacetimes
characterised by an initial phase either of exponential or of power-law
expansion. The states we obtain can be interpreted as being in thermal
equilibrium at the time when the scale factor a has a specific value a=a_0. In
the case a_0=0, these states fulfil a strict KMS condition on the boundary of
the spacetime, which is either a cosmological horizon, or a Big Bang
hypersurface. Furthermore, in the conformally invariant case, they are
conformal KMS states on the full spacetime. However, they provide a natural
notion of an approximate KMS state also in the remaining cases, especially for
massive fields. On the technical side, our results are based on a
bulk-to-boundary reconstruction technique already successfully applied in the
scalar case and here proven to be suitable also for spinor fields. The
potential applications of the states we find range over a broad spectrum, but
they appear to be suited to discuss in particular thermal phenomena such as the
cosmic neutrino background or the quantum state of dark matter.Comment: 42 page | Approximate KMS states for scalar and spinor fields in
Friedmann-Robertson-Walker spacetimes | approximate kms states for scalar and spinor fields in friedmann-robertson-walker spacetimes | hadamard dirac spinor spatially friedmann robertson walker spacetimes characterised exponential expansion. interpreted fulfil strict spacetime cosmological horizon bang hypersurface. conformally conformal spacetime. notion approximate massive fields. reconstruction successfully proven spinor fields. broad suited phenomena cosmic | non_dup | [] |
2161659 | 10.1007/s00023-011-0112-5 | A technically convenient signature of Anderson localization is exponential
decay of the fractional moments of the Green function within appropriate energy
ranges. We consider a random Hamiltonian on a lattice whose randomness is
generated by the sign-indefinite single-site potential, which is however
sign-definite at the boundary of its support. For this class of Anderson
operators we establish a finite-volume criterion which implies that above
mentioned the fractional moment decay property holds. This constructive
criterion is satisfied at typical perturbative regimes, e. g. at spectral
boundaries which satisfy 'Lifshitz tail estimates' on the density of states and
for sufficiently strong disorder. We also show how the fractional moment method
facilitates the proof of exponential (spectral) localization for such random
potentials.Comment: 29 pages, 1 figure, to appear in AH | Anderson localization for a class of models with a sign-indefinite
single-site potential via fractional moment method | anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method | technically convenient signature anderson localization exponential fractional moments ranges. randomness indefinite definite support. anderson establish criterion fractional moment holds. constructive criterion satisfied perturbative regimes boundaries satisfy lifshitz tail sufficiently disorder. fractional moment facilitates exponential localization pages | non_dup | [] |
2182337 | 10.1007/s00023-011-0119-y | {Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion
with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths
have the same local regularity. Defining properly iterated integrals of $B$ is
a difficult task because of the low H\"older regularity index of its paths. Yet
rough path theory shows it is the key to the construction of a stochastic
calculus with respect to $B$, or to solving differential equations driven by
$B$.
We intend to show in a series of papers how to desingularize iterated
integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure
defined by a limit in law procedure. Convergence is proved by using "standard"
tools of constructive field theory, in particular cluster expansions and
renormalization. These powerful tools allow optimal estimates, and call for an
extension of Gaussian tools such as for instance the Malliavin calculus.
After a first introductory paper \cite{MagUnt1}, this one concentrates on the
details of the constructive proof of convergence for second-order iterated
integrals, also known as L\'evy area | From constructive field theory to fractional stochastic calculus. (II)
Constructive proof of convergence for the L\'evy area of fractional Brownian
motion with Hurst index $\alpha\in(1/8,1/4)$ | from constructive field theory to fractional stochastic calculus. (ii) constructive proof of convergence for the l\'evy area of fractional brownian motion with hurst index $\alpha\in(1/8,1/4)$ | fractional brownian hurst alpha paths regularity. defining properly iterated integrals older regularity paths. rough stochastic calculus solving intend papers desingularize iterated integrals singular perturbation procedure. proved constructive expansions renormalization. powerful call malliavin calculus. introductory cite magunt concentrates constructive iterated integrals | non_dup | [] |
2097032 | 10.1007/s00023-011-0120-5 | Random skew plane partitions of large size distributed according to an
appropriately scaled Schur process develop limit shapes. In the present work we
consider the limit of large random skew plane partitions where the inner
boundary approaches a piecewise linear curve with non-lattice slopes,
describing the limit shape and the local fluctuations in various regions. This
analysis is fairly similar to that in [OR2], but we do find some new behavior.
For instance, the boundary of the limit shape is now a single smooth (not
algebraic) curve, whereas the boundary in [OR2] is singular. We also observe
the bead process introduced in [B] appearing in the asymptotics at the top of
the limit shape.Comment: 24 pages. This version to appear in Annales Henri Poincar | Random skew plane partitions with a piecewise periodic back wall | random skew plane partitions with a piecewise periodic back wall | skew partitions appropriately scaled schur shapes. skew partitions piecewise slopes describing regions. fairly behavior. algebraic singular. bead appearing asymptotics pages. annales henri poincar | non_dup | [] |
2162611 | 10.1007/s00023-011-0122-3 | The present article considers time symmetric initial data sets for the vacuum
Einstein field equations which in a neighbourhood of infinity have the same
massless part as that of some static initial data set. It is shown that the
solutions to the regular finite initial value problem at spatial infinity for
this class of initial data sets extend smoothly through the critical sets where
null infinity touches spatial infinity if and only if the initial data sets
coincide with static data in a neighbourhood of infinity. This result
highlights the special role played by static data among the class of initial
data sets for the Einstein field equations whose development gives rise to a
spacetime with a smooth conformal compactification at null infinity.Comment: 25 page | Asymptotic simplicity and static data | asymptotic simplicity and static data | considers einstein neighbourhood infinity massless set. infinity extend smoothly infinity touches infinity coincide neighbourhood infinity. highlights played einstein spacetime conformal compactification | non_dup | [] |
2138581 | 10.1007/s00023-011-0124-1 | We investigate the properties of the zeros of the eigenfunctions on quantum
graphs (metric graphs with a Schr\"odinger-type differential operator). Using
tools such as scattering approach and eigenvalue interlacing inequalities we
derive several formulas relating the number of the zeros of the n-th
eigenfunction to the spectrum of the graph and of some of its subgraphs. In a
special case of the so-called dihedral graph we prove an explicit formula that
only uses the lengths of the edges, entirely bypassing the information about
the graph's eigenvalues. The results are explained from the point of view of
the dynamics of zeros of the solutions to the scattering problem.Comment: 34 pages, 12 figure | Dynamics of nodal points and the nodal count on a family of quantum
graphs | dynamics of nodal points and the nodal count on a family of quantum graphs | zeros eigenfunctions schr odinger eigenvalue interlacing inequalities derive formulas relating zeros eigenfunction subgraphs. dihedral lengths entirely bypassing eigenvalues. zeros pages | non_dup | [] |
2128764 | 10.1007/s00023-011-0125-0 | We consider co-rotational wave maps from (3+1) Minkowski space into the
three-sphere. This is an energy supercritical model which is known to exhibit
finite time blow up via self-similar solutions. The ground state self-similar
solution $f_0$ is known in closed form and based on numerics, it is supposed to
describe the generic blow up behavior of the system. In this paper we develop a
rigorous linear perturbation theory around $f_0$. This is an indispensable
prerequisite for the study of nonlinear stability of the self-similar blow up
which is conducted in a companion paper. In particular, we prove that $f_0$ is
linearly stable if it is mode stable. Furthermore, concerning the mode
stability problem, we prove new results that exclude the existence of unstable
eigenvalues with large imaginary parts and also, with real parts larger than
1/2. The remaining compact region is well-studied numerically and all available
results strongly suggest the nonexistence of unstable modes.Comment: 32 pages, 2 figures, acknowledgments adde | On stable self-similar blow up for equivariant wave maps: The linearized
problem | on stable self-similar blow up for equivariant wave maps: the linearized problem | rotational minkowski sphere. supercritical exhibit blow solutions. numerics supposed generic blow system. rigorous perturbation indispensable prerequisite blow companion paper. linearly stable. concerning exclude unstable eigenvalues imaginary numerically nonexistence unstable pages acknowledgments adde | non_dup | [] |
2184548 | 10.1007/s00023-011-0127-y | We conclude our analysis of bubble divergences in the flat spinfoam model. In
[arXiv:1008.1476] we showed that the divergence degree of an arbitrary
two-complex Gamma can be evaluated exactly by means of twisted cohomology.
Here, we specialize this result to the case where Gamma is the two-skeleton of
the cell decomposition of a pseudomanifold, and sharpen it with a careful
analysis of the cellular and topological structures involved. Moreover, we
explain in detail how this approach reproduces all the previous powercounting
results for the Boulatov-Ooguri (colored) tensor models, and sheds light on
algebraic-topological aspects of Gurau's 1/N expansion.Comment: 19 page | Bubble divergences: sorting out topology from cell structure | bubble divergences: sorting out topology from cell structure | bubble divergences spinfoam model. divergence gamma twisted cohomology. specialize gamma skeleton decomposition pseudomanifold sharpen careful topological involved. reproduces powercounting boulatov ooguri colored sheds algebraic topological gurau | non_dup | [] |
2194580 | 10.1007/s00023-011-0140-1 | We generalize key aspects of arXiv:1010.5367 (and also arXiv:1010.5327) to
the case of {\em massless} $\lambda \phi^{2n}$ quantum field theory on deSitter
spacetime. As in that paper, our key objective is to derive a suitable
"Mellin-Barnes-type" representation of deSitter correlation functions in a
deSitter-invariant state, which holds to arbitrary orders in perturbation
theory, and which incorporates renormalization. The representation is suitable
for the study of large distance/time properties of correlation functions. It is
arrived at via an analytic continuation from the corresponding objects on the
sphere, and, as in the massive case, relies on the use of graph-polynomials and
their properties, as well as other tools. However, the perturbation expansion
is organized somewhat differently in the massless case, due to the well-known
subtleties associated with the "zero-mode" of the quantum field. In particular,
the correlation functions do not possess a well-defined limit as the
self-coupling constant of the field goes to zero, reflecting the well-known
non-existence of a deSitter invariant state in the free massless scalar theory.
We establish that generic correlation functions cannot grow more than
polynomially in proper time for large time-like separations of the points. Our
results thus leave open the possibility of quantum induced IR-instabilities of
deSitter spacetime on very large time-scales.Comment: 40 pages, several figures, v2: added references, more discussion in
app.C and in proof of thm.1, other minor change | Massless interacting quantum fields in deSitter spacetime | massless interacting quantum fields in desitter spacetime | generalize massless lambda desitter spacetime. derive mellin barnes desitter desitter orders perturbation incorporates renormalization. functions. arrived analytic continuation sphere massive relies polynomials tools. perturbation organized somewhat differently massless subtleties field. possess goes reflecting desitter massless theory. establish generic grow polynomially proper separations points. leave instabilities desitter spacetime pages app.c thm. minor | non_dup | [] |
2188145 | 10.1007/s00023-011-0142-z | The sum of the first n energy levels of the planar Laplacian with constant
magnetic field of given total flux is shown to be maximal among triangles for
the equilateral triangle, under normalization of the ratio (moment of
inertia)/(area)^3 on the domain. The result holds for both Dirichlet and
Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary
conditions too. The square similarly maximizes the eigenvalue sum among
parallelograms, and the disk maximizes among ellipses. More generally, a domain
with rotational symmetry will maximize the magnetic eigenvalue sum among all
linear images of that domain. These results are new even for the ground state
energy (n=1).Comment: 19 pages, 1 figur | Sums of magnetic eigenvalues are maximal on rotationally symmetric
domains | sums of magnetic eigenvalues are maximal on rotationally symmetric domains | planar laplacian maximal triangles equilateral triangle normalization moment inertia domain. dirichlet neumann analogue robin gennes too. maximizes eigenvalue parallelograms maximizes ellipses. rotational maximize eigenvalue domain. .comment pages figur | non_dup | [] |
2184002 | 10.1007/s00023-011-0143-y | The 6j-symbol is a fundamental object from the re-coupling theory of SU(2)
representations. In the limit of large angular momenta, its asymptotics is
known to be described by the geometry of a tetrahedron with quantized lengths.
This article presents a new recursion formula for the square of the 6j-symbol.
In the asymptotic regime, the new recursion is shown to characterize the
closure of the relevant tetrahedron. Since the 6j-symbol is the basic building
block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we
also discuss how to generalize the method to derive more general recursion
relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured;
Annales Henri Poincare (2011 | A New Recursion Relation for the 6j-Symbol | a new recursion relation for the 6j-symbol | symbol representations. momenta asymptotics tetrahedron quantized lengths. presents recursion symbol. asymptotic recursion characterize closure tetrahedron. symbol ponzano regge generalize derive recursion pages title changed structured annales henri poincare | non_dup | [] |
2130864 | 10.1007/s00023-011-0144-x | Consider a small sample coupled to a finite number of leads, and assume that
the total (continuous) system is at thermal equilibrium in the remote past. We
construct a non-equilibrium steady state (NESS) by adiabatically turning on an
electrical bias between the leads. The main mathematical challenge is to show
that certain adiabatic wave operators exist, and to identify their strong limit
when the adiabatic parameter tends to zero. Our NESS is different from, though
closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle
approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971
regarding the (non)equivalence between the partitioned and partition-free
approaches | Adiabatic non-equilibrium steady states in the partition free approach | adiabatic non-equilibrium steady states in the partition free approach | remote past. steady ness adiabatically turning electrical leads. mathematical challenge adiabatic adiabatic tends zero. ness closely ness pillet ruelle approach. partly settle asked caroli equivalence partitioned partition | non_dup | [] |
2189645 | 10.1007/s00023-011-0145-9 | In this paper, we show that massless Dirac waves in the Schwarzschild
geometry decay to zero at a rate $t^{-2\lambda}$, where $\lambda=1, 2,...$ is
the angular momentum. Our technique is to use Chandrasekhar's separation of
variables whereby the Dirac equations split into two sets of wave equations.
For the first set, we show that the wave decays as $t^{-2\lambda}$. For the
second set, in general, the solutions tend to some explicit profile at the rate
$t^{-2\lambda}$. The decay rate of solutions of Dirac equations is achieved by
showing that the coefficient of the explicit profile is exactly zero. The key
ingredients in the proof of the decay rate of solutions for the first set of
wave equations are an energy estimate used to show the absence of bound states
and zero energy resonance and the analysis of the spectral representation of
the solutions. The proof of asymptotic behavior for the solutions of the second
set of wave equations relies on careful analysis of the Green's functions for
time independent Schr\"odinger equations associated with these wave equations.Comment: 45 page | Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry | asymptotic behavior of massless dirac waves in schwarzschild geometry | massless dirac schwarzschild lambda lambda momentum. chandrasekhar whereby dirac split equations. decays lambda tend lambda dirac zero. ingredients solutions. asymptotic relies careful schr odinger | non_dup | [] |
2181299 | 10.1007/s00023-011-0146-8 | We initiate the study of the spherically symmetric Einstein-Klein-Gordon
system in the presence of a negative cosmological constant, a model appearing
frequently in the context of high-energy physics. Due to the lack of global
hyperbolicity of the solutions, the natural formulation of dynamics is that of
an initial boundary value problem, with boundary conditions imposed at null
infinity. We prove a local well-posedness statement for this system, with the
time of existence of the solutions depending only on an invariant H^2-type norm
measuring the size of the Klein-Gordon field on the initial data. The proof
requires the introduction of a renormalized system of equations and relies
crucially on r-weighted estimates for the wave equation on asymptotically AdS
spacetimes. The results provide the basis for our companion paper establishing
the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this
system.Comment: 50 pages, v2: minor changes, to appear in Annales Henri Poincar\' | Self-gravitating Klein-Gordon fields in asymptotically Anti-de-Sitter
spacetimes | self-gravitating klein-gordon fields in asymptotically anti-de-sitter spacetimes | initiate spherically einstein klein gordon cosmological appearing frequently physics. hyperbolicity formulation imposed infinity. posedness statement norm measuring klein gordon data. renormalized relies crucially weighted asymptotically spacetimes. companion establishing asymptotic schwarzschild sitter pages minor annales henri poincar | non_dup | [] |
2193096 | 10.1007/s00023-011-0150-z | We consider the semiclassical asymptotics of the sum of negative eigenvalues
of the three-dimensional Pauli operator with an external potential and a
self-generated magnetic field $B$. We also add the field energy $\beta \int
B^2$ and we minimize over all magnetic fields. The parameter $\beta$
effectively determines the strength of the field. We consider the weak field
regime with $\beta h^{2}\ge {const}>0$, where $h$ is the semiclassical
parameter. For smooth potentials we prove that the semiclassical asymptotics of
the total energy is given by the non-magnetic Weyl term to leading order with
an error bound that is smaller by a factor $h^{1+\e}$, i.e. the subleading term
vanishes. However, for potentials with a Coulomb singularity the subleading
term does not vanish due to the non-semiclassical effect of the singularity.
Combined with a multiscale technique, this refined estimate is used in the
companion paper \cite{EFS3} to prove the second order Scott correction to the
ground state energy of large atoms and molecules.Comment: Small typos corrected on Sep 24, 201 | Second order semiclassics with self-generated magnetic fields | second order semiclassics with self-generated magnetic fields | semiclassical asymptotics eigenvalues pauli beta minimize fields. beta effectively determines field. beta const semiclassical parameter. potentials semiclassical asymptotics weyl i.e. subleading vanishes. potentials coulomb singularity subleading vanish semiclassical singularity. multiscale refined companion cite scott typos corrected | non_dup | [] |
2184125 | 10.1007/s00023-011-0151-y | The main goal of this work consists in showing that the analytic solutions
for a class of characteristic problems for the Einstein vacuum equations have
an existence region larger than the one provided by the Cauchy-Kowalevski
theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove
this result we first describe a geometric way of writing the vacuum Einstein
equations for the characteristic problems we are considering, in a gauge
characterized by the introduction of a double null cone foliation of the
spacetime. Then we prove that the existence region for the analytic solutions
can be extended to a larger region which depends only on the validity of the
apriori estimates for the Weyl equations, associated to the "Bel-Robinson
norms". In particular if the initial data are sufficiently small we show that
the analytic solution is global. Before showing how to extend the existence
region we describe the same result in the case of the Burger equation, which,
even if much simpler, nevertheless requires analogous logical steps required
for the general proof. Due to length of this work, in this paper we mainly
concentrate on the definition of the gauge we use and on writing in a
"geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski
theorem is adapted to the characteristic problem for the Einstein equations and
we describe how the existence region can be extended in the case of the Burger
equation. Finally we describe the structure of the extension proof in the case
of the Einstein equations. The technical parts of this last result is the
content of a second paper.Comment: 68 page | Local and Global Analytic Solutions for a Class of Characteristic
Problems of the Einstein Vacuum Equations in the "Double Null Foliation
Gauge" | local and global analytic solutions for a class of characteristic problems of the einstein vacuum equations in the "double null foliation gauge" | goal analytic einstein cauchy kowalevski intrinsic hyperbolicity einstein equations. geometric writing einstein cone foliation spacetime. analytic validity apriori weyl robinson norms sufficiently analytic global. extend burger simpler nevertheless analogous logical proof. concentrate writing geometric einstein cauchy kowalevski adapted einstein burger equation. einstein equations. | non_dup | [] |
2191138 | 10.1007/s00023-011-0156-6 | The conventional approach to the infrared problem in perturbative quantum
electrodynamics relies on the concept of inclusive collision cross-sections. A
non-perturbative variant of this notion was introduced in algebraic quantum
field theory. Relying on these insights, we take first steps towards a
non-perturbative construction of inclusive collision cross-sections in the
massless Nelson model. We show that our proposal is consistent with the
standard scattering theory in the absence of the infrared problem and discuss
its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\' | Towards a construction of inclusive collision cross-sections in the
massless Nelson model | towards a construction of inclusive collision cross-sections in the massless nelson model | infrared perturbative electrodynamics relies inclusive collision sections. perturbative variant notion algebraic theory. relying insights perturbative inclusive collision massless nelson model. proposal infrared infrared singular pages latex. appeared ann. henri poincar | non_dup | [] |
2194596 | 10.1007/s00023-012-0171-2 | We propose a spectral curve describing torus knots and links in the B-model.
In particular, the application of the topological recursion to this curve
generates all their colored HOMFLY invariants. The curve is obtained by
exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved
conifold, and should be regarded as the mirror of the topological D-brane
associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we
derive the curve as the large N limit of the matrix model computing torus knot
invariants.Comment: 30 pages + appendix, 3 figure | Torus knots and mirror symmetry | torus knots and mirror symmetry | propose describing torus knots links model. topological recursion generates colored homfly invariants. exploiting resolved conifold regarded mirror topological brane torus knots gopakumar vafa duality. derive torus knot pages | non_dup | [] |
2134749 | 10.1007/s00023-012-0184-x | In a previous paper, we presented a matrix model reproducing the topological
string partition function on an arbitrary given toric Calabi-Yau manifold.
Here, we study the spectral curve of our matrix model and thus derive, upon
imposing certain minimality assumptions on the spectral curve, the large volume
limit of the BKMP "remodeling the B-model" conjecture, the claim that
Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the
spectral invariants of its mirror curve.Comment: 1+37 page | A matrix model for the topological string II: The spectral curve and
mirror geometry | a matrix model for the topological string ii: the spectral curve and mirror geometry | reproducing topological partition toric calabi manifold. derive imposing minimality assumptions bkmp remodeling conjecture claim gromov witten invariants toric calabi coincide invariants mirror | non_dup | [] |
9040725 | 10.1007/s00023-012-0189-5 | Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity | Schrödinger operators with δ and δ′-potentials supported on hypersurfaces | schrödinger operators with δ and δ′-potentials supported on hypersurfaces | adjoint schrödinger potentials hypersurface explicitly conditions. regularity analogues birman–schwinger variant krein’s shown. schatten–von neumann powers resolvents schrödinger potentials schrödinger singular proved. immediate completeness unitary equivalence absolutely singularly perturbed unperturbed schrödinger operators. proofs theorems algebraic considerations elliptic regularity | non_dup | [] |
20326367 | 10.1007/s00023-012-0195-7 | Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative {Mathematical expression} gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated with the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras | Instanton Counting and Wall-Crossing for Orbifold Quivers | instanton counting and wall-crossing for orbifold quivers | noncommutative donaldson thomas invariants abelian orbifold singularities enumeration instanton noncommutative mathematical mckay correspondence identifies instanton counting counting framed representations quiver naturally singularity. extend constructions partition refined motivic noncommutative donaldson thomas invariants coulomb branch orbifold data. notion virtual instanton quiver symplectic governs crossing context. mckay correspondence naturally connects formalism crossing monodromy algebras | non_dup | [] |
2245091 | 10.1007/s00023-012-0198-4 | Let (M,g) be a n-dimensional compact Riemannian manifold. We consider the
magnetic deformations of semiclassical Schrodinger operators on M for a family
of magnetic potentials that depends smoothly on $k$ parameters $u$, for $k \geq
n$, and satisfies a generic admissibility condition. Define the deformed
Schrodinger eigenfunctions to be the $u$-parametrized semiclassical family of
functions on M that is equal to the unitary magnetic Schrodinger propagator
applied to the Schrodinger eigenfunctions. The main result of this article
states that the $L^2$ norms in $u$ of the deformed Schrodinger eigenfunctions
are bounded above and below by constants, uniformly on $M$ and in $\hbar$. In
particular, the result shows that this non-random perturbation "kills" the
blow-up of eigenfunctions. We give, as applications, an eigenfunction
restriction bound and a quantum ergodicity result.Comment: To appear in Annales Henri Poincar\'e. 23 pages. Background
information on semiclassical wavefronts and eigenfunction concentration has
been added. Some notational changes made as well. Further changes made were
suggested by the refere | Averaged Pointwise Bounds for Deformations of Schrodinger Eigenfunctions | averaged pointwise bounds for deformations of schrodinger eigenfunctions | riemannian manifold. deformations semiclassical schrodinger potentials smoothly satisfies generic admissibility condition. deformed schrodinger eigenfunctions parametrized semiclassical unitary schrodinger propagator schrodinger eigenfunctions. norms deformed schrodinger eigenfunctions uniformly hbar perturbation kills blow eigenfunctions. eigenfunction restriction ergodicity annales henri poincar pages. semiclassical wavefronts eigenfunction added. notational well. refere | non_dup | [] |
2246221 | 10.1007/s00023-012-0200-1 | We construct time-dependent wave operators for Schr\"{o}dinger equations with
long-range potentials on a manifold $M$ with asymptotically conic structure. We
use the two space scattering theory formalism, and a reference operator on a
space of the form $\mathbb{R} \times \partial M$, where $\partial M$ is the
boundary of $M$ at infinity. We construct exact solutions to the
Hamilton-Jacobi equation on the reference system $\mathbb{R} \times \partial
M$, and prove the existence of the modified wave operators.Comment: 27 page | Existence of wave operators with time-dependent modifiers for the
Sch\"odinger equations with long-range potentials on scattering manifolds | existence of wave operators with time-dependent modifiers for the sch\"odinger equations with long-range potentials on scattering manifolds | schr dinger potentials manifold asymptotically conic structure. formalism mathbb infinity. hamilton jacobi mathbb | non_dup | [] |
9260650 | 10.1007/s00023-012-0201-0 | Using the methods developed for the Bianchi I case we have shown that a
boostrap argument is also suitable to treat the future non-linear stability for
reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types
II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution
with dust and the Ellis-MacCallum solution respectively. We have thus
generalized the results obtained by Rendall and Uggla in the case of locally
rotationally symmetric Bianchi II spacetimes to the reflection symmetric case.
However we needed to assume small data. For Bianchi VI$_0$ there is no
analogous previous result.Comment: 30 page | Future non-linear stability for reflection symmetric solutions of the
Einstein-Vlasov system of Bianchi types II and VI$_0$ | future non-linear stability for reflection symmetric solutions of the einstein-vlasov system of bianchi types ii and vi$_0$ | bianchi boostrap argument treat reflection einstein vlasov bianchi asymptotic collins stewart ellis maccallum respectively. rendall uggla locally rotationally bianchi spacetimes reflection case. data. bianchi analogous | non_dup | [] |
5259088 | 10.1007/s00023-012-0204-x | We analyze general enough models of repeated indirect measurements in which a
quantum system interacts repeatedly with randomly chosen probes on which Von
Neumann direct measurements are performed. We prove, under suitable hypotheses,
that the system state probability distribution converges after a large number
of repeated indirect measurements, in a way compatible with quantum wave
function collapse. Similarly a modified version of the system density matrix
converges. We show that the convergence is exponential with a rate given by
some relevant mean relative entropies. We also prove that, under appropriate
rescaling of the system and probe interactions, the state probability
distribution and the system density matrix are solutions of stochastic
differential equations modeling continuous-time quantum measurements. We
analyze the large time convergence of these continuous-time processes and prove
convergence.Comment: 44 pages, no figur | Repeated quantum non-demolition measurements: convergence and
continuous-time limit | repeated quantum non-demolition measurements: convergence and continuous-time limit | analyze repeated indirect interacts repeatedly randomly probes neumann performed. hypotheses converges repeated indirect compatible collapse. converges. exponential entropies. rescaling stochastic measurements. analyze pages figur | non_dup | [] |
47101032 | 10.1007/s00023-012-0211-y | International audienceIn this paper we consider a variational problem related to a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants | Ground States for a Stationary Mean-Field Model for a Nucleon | ground states for a stationary mean-field model for a nucleon | audiencein variational nucleon interacting omega sigma mesons nucleus. relativistic nonrelativistic nonrelativistic physics. | non_dup | [] |
5242701 | 10.1007/s00023-012-0213-9 | We show how to approximate Dirac dynamics for electronic initial states by
semi- and non-relativistic dynamics. To leading order, these are generated by
the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is
related to $\sqrt{m^2 + \xi^2}$ and $\xi^2 / 2m$, respectively. Higher-order
corrections can in principle be computed to any order in the small parameter
v/c which is the ratio of typical speeds to the speed of light. Our results
imply the dynamics for electronic and positronic states decouple to any order
in v/c << 1.
To decide whether to get semi- or non-relativistic effective dynamics, one
needs to choose a scaling for the kinetic momentum operator. Then the effective
dynamics are derived using space-adiabatic perturbation theory by Panati et. al
with the novel input of a magnetic pseudodifferential calculus adapted to
either the semi- or non-relativistic scaling.Comment: 42 page | Semi- and Non-relativistic Limit of the Dirac Dynamics with External
Fields | semi- and non-relativistic limit of the dirac dynamics with external fields | approximate dirac relativistic dynamics. relativistic pauli sqrt respectively. speeds light. imply positronic decouple decide relativistic operator. adiabatic perturbation panati pseudodifferential calculus adapted relativistic | non_dup | [] |
8780902 | 10.1007/s00023-012-0214-8 | We study driven systems with possible population inversion and we give
optimal bounds on the relative occupations in terms of released heat. A precise
meaning to Landauer's blowtorch theorem (1975) is obtained stating that
nonequilibrium occupations are essentially modified by kinetic effects. Towards
very low temperatures we apply a Freidlin-Wentzel type analysis for continuous
time Markov jump processes. It leads to a definition of dominant states in
terms of both heat and escape rates.Comment: 11 pages; v2: minor changes, 1 reference adde | Heat bounds and the blowtorch theorem | heat bounds and the blowtorch theorem | inversion bounds occupations released heat. precise meaning landauer blowtorch stating nonequilibrium occupations essentially effects. freidlin wentzel markov jump processes. escape pages minor adde | non_dup | [] |
2255186 | 10.1007/s00023-012-0222-8 | In the framework of non-relativistic QED, we show that the renormalized mass
of the electron (after having taken into account radiative corrections) appears
as the kinematic mass in its response to an external potential force.
Specifically, we study the dynamics of an electron in a slowly varying external
potential and with slowly varying initial conditions and prove that, for a long
time, it is accurately described by an associated effective dynamics of a
Schr\"odinger electron in the same external potential and for the same initial
data, with a kinetic energy operator determined by the renormalized dispersion
law of the translation-invariant QED model.Comment: 22 pages, AMS Late | Effective dynamics of an electron coupled to an external potential in
non-relativistic QED | effective dynamics of an electron coupled to an external potential in non-relativistic qed | relativistic renormalized radiative kinematic force. slowly slowly accurately schr odinger renormalized translation pages | non_dup | [] |
2158450 | 10.1007/s00023-012-0223-7 | In this article, I study the diffusive behavior for a quantum test particle
interacting with a dilute background gas. The model I begin with is a reduced
picture for the test particle dynamics given by a quantum linear Boltzmann
equation in which the gas particle scattering is assumed to occur through a
hard-sphere interaction. The state of the particle is represented by a density
matrix that evolves according to a translation-covariant Lindblad equation. The
main result is a proof that the particle's position distribution converges to a
Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version
and corrected an error in the proof of Proposition 7. | Diffusive limit for a quantum linear Boltzmann dynamics | diffusive limit for a quantum linear boltzmann dynamics | diffusive interacting dilute gas. begin picture boltzmann sphere interaction. evolves translation covariant lindblad equation. converges diffusive pages. restructured corrected | non_dup | [] |
9324134 | 10.1007/s00023-013-0233-0 | The Eynard-Orantin topological recursion relies on the geometry of a Riemann
surface S and two meromorphic functions x and y on S. To formulate the
recursion, one must assume that x has only simple ramification points. In this
paper we propose a generalized topological recursion that is valid for x with
arbitrary ramification. We justify our proposal by studying degenerations of
Riemann surfaces. We check in various examples that our generalized recursion
is compatible with invariance of the free energies under the transformation
(x,y) -> (y,x), where either x or y (or both) have higher order ramification,
and that it satisfies some of the most important properties of the original
recursion. Along the way, we show that invariance under (x,y) -> (y,x) is in
fact more subtle than expected; we show that there exists a number of counter
examples, already in the case of the original Eynard-Orantin recursion, that
deserve further study.Comment: 26 pages, 2 figure | A generalized topological recursion for arbitrary ramification | a generalized topological recursion for arbitrary ramification | eynard orantin topological recursion relies riemann meromorphic formulate recursion ramification points. propose topological recursion valid ramification. justify proposal studying degenerations riemann surfaces. check recursion compatible invariance ramification satisfies recursion. invariance subtle counter eynard orantin recursion deserve pages | non_dup | [] |
24771571 | 10.1007/s00023-013-0234-z | We develop a general framework for the quantization of bosonic and fermionic
field theories on affine bundles over arbitrary globally hyperbolic spacetimes.
All concepts and results are formulated using the language of category theory,
which allows us to prove that these models satisfy the principle of general
local covariance. Our analysis is a preparatory step towards a full-fledged
quantization scheme for the Maxwell field, which emphasises the affine bundle
structure of the bundle of principal U(1)-connections. As a by-product, our
construction provides a new class of exactly tractable locally covariant
quantum field theories, which are a mild generalization of the linear ones. We
also show the existence of a functorial assignment of linear quantum field
theories to affine ones. The identification of suitable algebra homomorphisms
enables us to induce whole families of physical states (satisfying the
microlocal spectrum condition) for affine quantum field theories by pulling
back quasi-free Hadamard states of the underlying linear theories.Comment: 34 pages, no figures; v2: 35 pages, compatible with version to be
published in Annales Henri Poincar | Quantum field theory on affine bundles | quantum field theory on affine bundles | quantization bosonic fermionic affine bundles globally hyperbolic spacetimes. concepts formulated satisfy covariance. preparatory fledged quantization maxwell emphasises affine bundle bundle principal connections. tractable locally covariant mild generalization ones. functorial assignment affine ones. homomorphisms enables induce families satisfying microlocal affine pulling quasi hadamard pages pages compatible annales henri poincar | non_dup | [] |
5251615 | 10.1007/s00023-013-0235-y | We consider a general class of random matrices whose entries are centred
random variables, independent up to a symmetry constraint. We establish precise
high-probability bounds on the averages of arbitrary monomials in the resolvent
matrix entries. Our results generalize the previous results of [5,16,17] which
constituted a key step in the proof of the local semicircle law with optimal
error bound in mean-field random matrix models. Our bounds apply to random band
matrices, and improve previous estimates from order 2 to order 4 in the cases
relevant for applications. In particular, they lead to a proof of the diffusion
approximation for the magnitude of the resolvent of random band matrices. This,
in turn, implies new delocalization bounds on the eigenvectors. The
applications are presented in a separate paper [3] | Averaging Fluctuations in Resolvents of Random Band Matrices | averaging fluctuations in resolvents of random band matrices | entries centred constraint. establish precise bounds averages monomials resolvent entries. generalize constituted semicircle models. bounds applications. resolvent matrices. delocalization bounds eigenvectors. | non_dup | [] |
9261474 | 10.1007/s00023-013-0236-x | We show how general principles of symmetry in quantum mechanics lead to
twisted notions of a group representation. This framework generalizes both the
classical 3-fold way of real/complex/quaternionic representations as well as a
corresponding 10-fold way which has appeared in condensed matter and nuclear
physics. We establish a foundation for discussing continuous families of
quantum systems. Having done so, topological phases of quantum systems can be
defined as deformation classes of continuous families of gapped Hamiltonians.
For free particles there is an additional algebraic structure on the
deformation classes leading naturally to notions of twisted equivariant
K-theory. In systems with a lattice of translational symmetries we show that
there is a canonical twisting of the equivariant K-theory of the Brillouin
torus. We give precise mathematical definitions of two invariants of the
topological phases which have played an important role in the study of
topological insulators. Twisted equivariant K-theory provides a finer
classification of topological insulators than has been previously available.Comment: 93 pages, 1 figure; v2 has minor corrections and clarifications for
publication in AH | Twisted equivariant matter | twisted equivariant matter | principles mechanics twisted notions representation. generalizes quaternionic representations appeared condensed physics. establish foundation discussing families systems. topological deformation families gapped hamiltonians. algebraic deformation naturally notions twisted equivariant theory. translational symmetries canonical twisting equivariant brillouin torus. precise mathematical definitions invariants topological played topological insulators. twisted equivariant finer topological insulators pages minor clarifications publication | non_dup | [] |
9324710 | 10.1007/s00023-013-0240-1 | In this paper, we extend the work in
\cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic
conditions on the second fundamental form, and we also give an $L^{6}-$norm
bound for the difference between general data and Extreme Kerr data or Extreme
Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when
the target has non-positive curvature. In particular, we give the first proof
of the strict mass/angular momentum/charge inequality for axisymmetric
Einstein/Maxwell data which is not identical with the extreme Kerr-Newman
solution.Comment: 27 page | Convexity of reduced energy and mass angular momentum inequalities | convexity of reduced energy and mass angular momentum inequalities | extend cite cite chrusliwe cite chrusco cite weaken asymptotic norm extreme kerr extreme kerr newman proving convexity renormalized dirichlet curvature. strict inequality axisymmetric einstein maxwell extreme kerr newman | non_dup | [] |
9262339 | 10.1007/s00023-013-0241-0 | We study the level spacing distribution for the spectrum of a point scatterer
on a flat torus. In the 2-dimensional case, we show that in the weak coupling
regime the eigenvalue spacing distribution coincides with that of the spectrum
of the Laplacian (ignoring multiplicties), by showing that the perturbed
eigenvalues generically clump with the unperturbed ones on the scale of the
mean level spacing. We also study the three dimensional case, where the
situation is very different.Comment: 25 page | On the eigenvalue spacing distribution for a point scatterer on the flat
torus | on the eigenvalue spacing distribution for a point scatterer on the flat torus | spacing scatterer torus. eigenvalue spacing coincides laplacian ignoring multiplicties perturbed eigenvalues generically clump unperturbed spacing. | non_dup | [] |
24946190 | 10.1007/s00023-013-0253-9 | In this paper we consider lattice systems coupled by local interactions. We
prove invariant manifold theorems for whiskered tori (we recall that whiskered
tori are quasi-periodic solutions with exponentially contracting and expanding
directions in the linearized system). The invariant manifolds we construct
generalize the usual (strong) (un) stable manifolds and allow us to consider
also non-resonant manifolds. We show that if the whiskered tori are localized
near a collection of specific sites, then so are the invariant manifolds.
We recall that the existence of localized whiskered tori has recently been
proven for symplectic maps and flows in Fontich et. al. (submitted), but our
results do not need that the systems are symplectic. For simplicity we will
present first the main results for maps, but we will show tha the result for
maps imply the results for flows. It is also true that the results for flows
can be proved directly following the same ideas.Comment: This version corrects a bibliographical typo that appears in the
version published in Annales Henri Poincare: Reference [FdlLS12] was wrongly
listed by the publisher as "submitted to Jour. Diff. Equ." in the published
version. Reference [FdlLS12] has not been submitted to Jour. Diff. Eq | Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices
with Decaying Interaction | localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction | interactions. manifold theorems whiskered tori whiskered tori quasi exponentially contracting expanding directions linearized manifolds generalize usual manifolds resonant manifolds. whiskered tori localized manifolds. localized whiskered tori proven symplectic flows fontich submitted symplectic. simplicity imply flows. flows proved corrects bibliographical typo annales henri poincare fdlls wrongly listed publisher submitted jour. diff. equ. version. fdlls submitted jour. diff. | non_dup | [] |
2555638 | 10.1007/s00023-013-0254-8 | We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
$q$ of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
completely revised: the results of v1 and v2 are extended to all order | Explicit solution of the (quantum) elliptic Calogero-Sutherland model | explicit solution of the (quantum) elliptic calogero-sutherland model | derive formulas eigenfunctions eigenvalues elliptic calogero sutherland infinite orders parameters. eigenfunctions elliptic deformation jack polynomials. nome elliptic integer pages. order. pages. extended. pages. revised | non_dup | [] |
2097051 | 10.1007/s00023-013-0256-6 | We study worldsheet conformal invariance for bosonic string propagating in a
curved background using the hamiltonian formalism. In order to formulate the
problem in a background independent manner we first rewrite the worldsheet
theory in a language where it describes a single particle moving in an
infinite-dimensional curved spacetime. This language is developed at a formal
level without regularizing the infinite-dimensional traces. Then we adopt
DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of
quantum mechanics in the present context. Given the expressions for the
classical Virasoro generators, this procedure enables us to define the
coordinate invariant quantum analogues which we call DeWitt-Virasoro
generators. This framework also enables us to calculate the invariant matrix
elements of an arbitrary operator constructed out of the DeWitt-Virasoro
generators between two arbitrary scalar states. Using these tools we further
calculate the DeWitt-Virasoro algebra in spin-zero representation. The result
is given by the Witt algebra with additional anomalous terms that vanish for
Ricci-flat backgrounds. Further analysis need to be performed in order to
precisely relate this with the beta function computation of Friedan and others.
Finally, we explain how this analysis improves the understanding of showing
conformal invariance for certain pp-wave that has been recently discussed using
hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no
change in conclusio | On a coordinate independent description of string worldsheet theory | on a coordinate independent description of string worldsheet theory | worldsheet conformal invariance bosonic propagating curved formalism. formulate manner rewrite worldsheet describes moving infinite curved spacetime. formal regularizing infinite traces. adopt dewitt phys.rev. coordinate formulation mechanics context. expressions virasoro generators enables coordinate analogues call dewitt virasoro generators. enables dewitt virasoro generators states. dewitt virasoro representation. witt anomalous vanish ricci backgrounds. precisely relate beta friedan others. improves conformal invariance pages reorganization elaborate explanation conclusio | non_dup | [] |
38255925 | 10.1007/s00023-013-0267-3 | We present a new rigorous approach based on Orlicz spaces for
the description of the statistics of large regular statistical systems, both
classical and quantum. The pair of Orlicz spaces we explicitly use are,
respectively, built on the exponential function (for the description of regular
observables) and on an entropic type function (for the corresponding
states). They form a dual pair (both for classical and quantum systems).
This pair has the advantage of being general enough to encompass regular
observables, and specific enough for the latter Orlicz space to select
states with a well-defined entropy function. Moreover for small quantum
systems, this pair is shown to agree with the classical pairing of bounded
linear operators on a Hilbert space, and the trace-class operators.Grant Number N N202 208238; Foundation
for Polish Science TEAM project cofinanced by the EU European Regional
Development Fund for W.A. Majewski; National Research
Foundation for L.E. Labuschagnehttp://dx.doi.org/10.1007/s00023-013-0267-3http://www.springer.com/birkhauser/physics/journal/2 | On applications of Orlicz spaces to statistical physics | on applications of orlicz spaces to statistical physics | rigorous orlicz quantum. orlicz explicitly built exponential observables entropic advantage encompass observables orlicz select function. agree pairing hilbert trace operators.grant foundation polish team cofinanced fund w.a. majewski foundation l.e. labuschagnehttp | non_dup | [] |
24794346 | 10.1007/s00023-013-0273-5 | In one and two spatial dimensions there is a logical possibility for
identical quantum particles different from bosons and fermions, obeying
intermediate or fractional (anyon) statistics. We consider applications of a
recent Lieb-Thirring inequality for anyons in two dimensions, and derive new
Lieb-Thirring inequalities for intermediate statistics in one dimension with
implications for models of Lieb-Liniger and Calogero-Sutherland type. These
inequalities follow from a local form of the exclusion principle valid for such
generalized exchange statistics.Comment: Revised and accepted version. 49 pages, 2 figure | Local exclusion and Lieb-Thirring inequalities for intermediate and
fractional statistics | local exclusion and lieb-thirring inequalities for intermediate and fractional statistics | logical bosons fermions obeying fractional anyon statistics. lieb thirring inequality anyons derive lieb thirring inequalities lieb liniger calogero sutherland type. inequalities exclusion valid revised version. pages | non_dup | [] |
24796368 | 10.1007/s00023-013-0276-2 | A class of curves with special conformal properties (conformal curves) is
studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data
for the conformal curves can be prescribed so that the resulting congruence of
curves extends smoothly to future and past null infinity. The formation of
conjugate points on these congruences is examined. The results of this analysis
are expected to be of relevance for the discussion of the Reissner-Nordstr\"om
spacetime as a solution to the conformal field equations and for the global
numerical evaluation of static black hole spacetimes.Comment: 32 pages, 2 figure | A class of conformal curves in the Reissner-Nordstr\"om spacetime | a class of conformal curves in the reissner-nordstr\"om spacetime | conformal conformal reissner nordstr spacetime. conformal prescribed congruence extends smoothly infinity. conjugate congruences examined. relevance reissner nordstr spacetime conformal pages | non_dup | [] |
24795566 | 10.1007/s00023-013-0279-z | We study a functional on the boundary of a compact Riemannian 3-manifold of
nonnegative scalar curvature. The functional arises as the second variation of
the Wang-Yau quasi-local energy in general relativity. We prove that the
functional is positive definite on large coordinate spheres, and more general
on nearly round surfaces including large constant mean curvature spheres in
asymptotically flat 3-manifolds with positive mass; it is also positive
definite on small geodesics spheres, whose centers do not have vanishing
curvature, in Riemannian 3-manifolds of nonnegative scalar curvature. We also
give examples of functions H, which can be made arbitrarily close to the
constant 2, on the standard sphere such that the boundary data consisting of
the standard spherical metric and H has positive Brown-York mass while the
associated functional is negative somewhere.Comment: 36 page | On second variation of Wang-Yau quasi-local energy | on second variation of wang-yau quasi-local energy | riemannian manifold nonnegative curvature. arises quasi relativity. definite coordinate spheres nearly round curvature spheres asymptotically manifolds definite geodesics spheres centers vanishing curvature riemannian manifolds nonnegative curvature. arbitrarily sphere consisting spherical brown | non_dup | [] |
48333817 | 10.1007/s00023-013-0283-3 | International audienceIn this article, we consider quantum crystals with defects in the reduced Hartree-Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration. The perturbation is assumed to be small in amplitude, but need not be localized in a specific region of space or have any spatial invariance. Assuming Yukawa interactions, we prove the existence of an electronic ground state, solution of the self-consistent field equation. Next, by studying precisely the decay properties of this solution for local defects, we are able to expand the density of states of the nonlinear Hamiltonian of a system with a random perturbation of Anderson-Bernoulli type, in the limit of low concentration of defects. One important step in the proof of our results is the analysis of the dielectric response of the crystal to an effective charge perturbation | The Reduced Hartree-Fock Model for Short-Range Quantum Crystals with Nonlocal Defects | the reduced hartree-fock model for short-range quantum crystals with nonlocal defects | audiencein crystals defects hartree fock framework. nuclei supposed arranged configuration. perturbation localized invariance. yukawa equation. studying precisely defects expand perturbation anderson bernoulli defects. dielectric perturbation | non_dup | [] |
24942710 | 10.1007/s00023-013-0285-1 | We consider the Landau Hamiltonian perturbed by a long-range electric
potential $V$. The spectrum of the perturbed operator consists of eigenvalue
clusters which accumulate to the Landau levels. First, we obtain an estimate of
the rate of the shrinking of these clusters to the Landau levels as the number
of the cluster $q$ tends to infinity. Further, we assume that there exists an
appropriate $\V$, homogeneous of order $-\rho$ with $\rho \in (0,1)$, such that
$V(x) = \V(x) + O(|x|^{-\rho - \epsilon})$, $\epsilon > 0$, as $|x| \to
\infty$, and investigate the asymptotic distribution of the eigenvalues within
a given cluster, as $q \to \infty$. We obtain an explicit description of the
asymptotic density of the eigenvalues in terms of the mean-value transform of
$\V$.Comment: 27 pages, to appear in Ann. H Poincar\' | A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian | a trace formula for long-range perturbations of the landau hamiltonian | landau perturbed perturbed eigenvalue accumulate landau levels. shrinking landau tends infinity. homogeneous epsilon epsilon infty asymptotic eigenvalues infty asymptotic eigenvalues transform .comment pages ann. poincar | non_dup | [] |
24795833 | 10.1007/s00023-013-0287-z | We derive rigorously the leading asymptotics of the so-called Anderson
integral in the thermodynamic limit for one-dimensional, non-relativistic,
spin-less Fermi systems. The coefficient, $\gamma$, of the leading term is
computed in terms of the S-matrix. This implies a lower and an upper bound on
the exponent in Anderson's orthogonality catastrophe, $\tilde
CN^{-\tilde\gamma}\leq \mathcal{D}_N\leq CN^{-\gamma}$ pertaining to the
overlap, $\mathcal{D}_N$, of ground states of non-interacting fermions.Comment: 39 page | Anderson's Orthogonality Catastrophe for One-dimensional Systems | anderson's orthogonality catastrophe for one-dimensional systems | derive rigorously asymptotics anderson thermodynamic relativistic fermi systems. gamma matrix. exponent anderson orthogonality catastrophe tilde tilde gamma mathcal gamma pertaining overlap mathcal interacting | non_dup | [] |
24948043 | 10.1007/s00023-013-0289-x | We define a double affine $Q$-dependent braid group. This group is
constructed by appending to the braid group a set of operators $Q_i$, before
extending it to an affine $Q$-dependent braid group. We show specifically that
the elliptic braid group and the double affine Hecke algebra (DAHA) can be
obtained as quotient groups. Complementing this we present a pictorial
representation of the double affine $Q$-dependent braid group based on ribbons
living in a toroid. We show that in this pictorial representation we can fully
describe any DAHA. Specifically, we graphically describe the parameter $q$ upon
which this algebra is dependent and show that in this particular representation
$q$ corresponds to a twist in the ribbon | Graphical Calculus for the Double Affine Q-Dependent Braid Group | graphical calculus for the double affine q-dependent braid group | affine braid group. appending braid extending affine braid group. elliptic braid affine hecke daha quotient groups. complementing pictorial affine braid ribbons living toroid. pictorial daha. graphically twist ribbon | non_dup | [] |
24951884 | 10.1007/s00023-013-0294-0 | We show how to relate the full quantum dynamics of a spin-1/2 particle on R^d
to a classical Hamiltonian dynamics on the enlarged phase space R^d x S^2 up to
errors of second order in the semiclassical parameter. This is done via an
Egorov-type theorem for normal Wigner-Weyl calculus for R^d [Lei10,Fol89]
combined with the Stratonovich-Weyl calculus for SU(2) [VGB89]. For a specific
class of Hamiltonians, including the Rabi- and Jaynes-Cummings model, we prove
an Egorov theorem for times much longer than the semiclassical time scale. We
illustrate the approach for a simple model of the Stern-Gerlach experiment.Comment: 24 page | Semiclassics for particles with spin via a Wigner-Weyl-type calculus | semiclassics for particles with spin via a wigner-weyl-type calculus | relate enlarged semiclassical parameter. egorov wigner weyl calculus stratonovich weyl calculus hamiltonians rabi jaynes cummings egorov semiclassical scale. illustrate stern gerlach | non_dup | [] |
24949110 | 10.1007/s00023-013-0296-y | The Penrose inequality in Minkowski is a geometric inequality relating the
total outer null expansion and the area of closed, connected and spacelike
codimension-two surfaces S in the Minkowski spacetime, subject to an additional
convexity assumption. In a recent paper, Brendle and Wang find a sufficient
condition for the validity of this Penrose inequality in terms of the geometry
of the orthogonal projection of S onto a constant time hyperplane. In this
work, we study the geometry of hypersurfaces in n-dimensional euclidean space
which are normal graphs over other surfaces and relate the intrinsic and
extrinsic geometry of the graph with that of the base hypersurface. These
results are used to rewrite Brendle and Wang's condition explicitly in terms of
the time height function of S over a hyperplane and the geometry of the
projection of S along its past null cone onto this hyperplane. We also include,
in an Appendix, a self-contained summary of known and new results on the
geometry of projections along the Killing direction of codimension
two-spacelike surfaces in a strictly static spacetime.Comment: 15 pages, 1 figure, Late | Geometry of normal graphs in Euclidean space and applications to the
Penrose inequality in Minkowski | geometry of normal graphs in euclidean space and applications to the penrose inequality in minkowski | penrose inequality minkowski geometric inequality relating outer spacelike codimension minkowski spacetime convexity assumption. brendle validity penrose inequality orthogonal projection hyperplane. hypersurfaces euclidean relate intrinsic extrinsic hypersurface. rewrite brendle explicitly hyperplane projection cone hyperplane. projections killing codimension spacelike strictly pages | non_dup | [] |
48210108 | 10.1007/s00023-013-0298-9 | 28 pagesInternational audienceThe interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive effective, lower-dimensional models which depend on the intensity of the magnetic field and curvatures. The results are used to establish complete asymptotic expansions for eigenvalues. Spectral stability properties based on Hardy-type inequalities induced by magnetic fields are also analysed | Magnetic effects in curved quantum waveguides | magnetic effects in curved quantum waveguides | pagesinternational audiencethe interplay tubular neighbourhoods euclidean shrinks point. proving norm resolvent derive curvatures. establish asymptotic expansions eigenvalues. hardy inequalities analysed | non_dup | [] |
24932998 | 10.1007/s00023-013-0302-4 | We consider homogeneous Bose gas in a large cubic box with periodic boundary
conditions, at zero temperature. We analyze its excitation spectrum in a
certain kind of a mean field infinite volume limit. We prove that under
appropriate conditions the excitation spectrum has the form predicted by the
Bogoliubov approximation. Our result can be viewed as an extension of the
result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes.Comment: Revised and extended version. 26 pages, 4 figures. To appear in
Annales Henri Poincar\' | Excitation spectrum of interacting bosons in the mean-field
infinite-volume limit | excitation spectrum of interacting bosons in the mean-field infinite-volume limit | homogeneous bose cubic temperature. analyze kind infinite limit. bogoliubov approximation. viewed seiringer math revised version. pages figures. annales henri poincar | non_dup | [] |
24992988 | 10.1007/s00023-014-0324-6 | The scaling and mass expansion (shortly 'sm-expansion') is a new axiom for
causal perturbation theory, which is a stronger version of a frequently used
renormalization condition in terms of Steinmann's scaling degree. If one
quantizes the underlying free theory by using a Hadamard function (which is
smooth in $m\geq 0$), one can reduce renormalization of a massive model to the
extension of a minimal set of mass-independent, almost homogeneously scaling
distributions by a Taylor expansion in the mass $m$. The sm-expansion is a
generalization of this Taylor expansion, which yields this crucial
simplification of the renormalization of massive models also for the case that
one quantizes with the Wightman two-point function, which contains a
$\log(-(m^2(x^2-ix^0 0))$-term. We construct the general solution of the new
system of axioms (i.e. the usual axioms of causal perturbation theory completed
by the sm-expansion), and illustrate the method for a divergent diagram which
contains a divergent subdiagram.Comment: v2: some explanations added; 26 pages; version to appear in Ann.
Henri Poincar | The scaling and mass expansion | the scaling and mass expansion | shortly axiom causal perturbation stronger frequently renormalization steinmann degree. quantizes hadamard renormalization massive homogeneously taylor generalization taylor crucial simplification renormalization massive quantizes wightman term. axioms i.e. usual axioms causal perturbation completed illustrate divergent divergent explanations pages ann. henri poincar | non_dup | [] |
24969195 | 10.1007/s00023-014-0335-3 | We construct an extensive adiabatic invariant for a Klein-Gordon chain in the
thermodynamic limit. In particular, given a fixed and sufficiently small value
of the coupling constant $a$, the evolution of the adiabatic invariant is
controlled up to times scaling as $\beta^{1/\sqrt{a}}$ for any large enough
value of the inverse temperature $\beta$. The time scale becomes a stretched
exponential if the coupling constant is allowed to vanish jointly with the
specific energy. The adiabatic invariance is exhibited by showing that the
variance along the dynamics, i.e. calculated with respect to time averages, is
much smaller than the corresponding variance over the whole phase space, i.e.
calculated with the Gibbs measure, for a set of initial data of large measure.
All the perturbative constructions and the subsequent estimates are consistent
with the extensive nature of the system.Comment: 60 pages. Minor corrections with respect to the first version. To
appear in Annales Henri Poincar\' | An extensive adiabatic invariant for the Klein-Gordon model in the
thermodynamic limit | an extensive adiabatic invariant for the klein-gordon model in the thermodynamic limit | extensive adiabatic klein gordon thermodynamic limit. sufficiently adiabatic beta sqrt beta stretched exponential vanish jointly energy. adiabatic invariance exhibited i.e. averages i.e. gibbs measure. perturbative constructions extensive pages. minor version. annales henri poincar | non_dup | [] |
24931528 | 10.1007/s00023-014-0337-1 | Our previous constructions of Borchers triples are extended to massless
scattering with nontrivial left and right components. A massless Borchers
triple is constructed from a set of left-left, right-right and left-right
scattering functions. We find a correspondence between massless left-right
scattering S-matrices and massive block diagonal S-matrices. We point out a
simple class of S-matrices with examples.
We study also the restriction of two-dimensional models to the lightray.
Several arguments for constructing strictly local two-dimensional nets are
presented and possible scenarios are discussed.Comment: 42 pages, 1 Tikz figure. The final version is available under Open
Access. An erratum concerning Definition 3.4(4) of the right-mixed
Yang-Baxter equation is available at
http://dx.doi.org/10.1007/s00023-014-0337-1 . This arXiv version contains the
corrected definitions and proposition | Integrable QFT and Longo-Witten endomorphisms | integrable qft and longo-witten endomorphisms | constructions borchers triples massless nontrivial components. massless borchers triple functions. correspondence massless massive diagonal matrices. examples. restriction lightray. arguments constructing strictly nets scenarios pages tikz figure. access. erratum concerning baxter corrected definitions | non_dup | [] |
73361144 | 10.1007/s00023-014-0345-1 | From quantum mechanical first principles only, we rigorously study the
time-evolution of a $N$-level atom (impurity) interacting with an external
monochromatic light source within an infinite system of free electrons at
thermal equilibrium (reservoir). In particular, we establish the relation
between the full dynamics of the compound system and the effective dynamics for
the $N$-level atom, which is studied in detail in [Bru-de Siqueira
Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370, 2012]. Together with
[Bru-de Siqueira Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370,
2012] the present paper yields a purely microscopic theory of optical pumping
in laser physics. The model we consider is general enough to describe gauge
invariant atom-reservoir interactions | Characterization of the Quasi-Stationary State of an Impurity Driven by
Monochromatic Light II - Microscopic Foundations | characterization of the quasi-stationary state of an impurity driven by monochromatic light ii - microscopic foundations | principles rigorously atom impurity interacting monochromatic infinite reservoir establish compound atom siqueira pedra westrich annales henri poincar siqueira pedra westrich annales henri poincar purely microscopic pumping physics. atom reservoir | non_dup | [] |
24981233 | 10.1007/s00023-014-0347-z | We study zero modes of Laplacians on compact and non-compact metric graphs
with general self-adjoint vertex conditions. In the first part of the paper the
number of zero modes is expressed in terms of the trace of a unitary matrix
$\mathfrak{S}$ that encodes the vertex conditions imposed on functions in the
domain of the Laplacian. In the second part a Dirac operator is defined whose
square is related to the Laplacian. In order to accommodate Laplacians with
negative eigenvalues it is necessary to define the Dirac operator on a suitable
Kre\u{\i}n space. We demonstrate that an arbitrary, self-adjoint quantum graph
Laplacian admits a factorisation into momentum-like operators in a
Kre\u{\i}n-space setting. As a consequence, we establish an index theorem for
the associated Dirac operator and prove that the zero-mode contribution in the
trace formula for the Laplacian can be expressed in terms of the index of the
Dirac operator | Zero modes of quantum graph Laplacians and an index theorem | zero modes of quantum graph laplacians and an index theorem | laplacians adjoint conditions. trace unitary mathfrak encodes imposed laplacian. dirac laplacian. accommodate laplacians eigenvalues dirac space. adjoint laplacian admits factorisation setting. establish dirac trace laplacian dirac | non_dup | [] |
24963796 | 10.1007/s00023-014-0358-9 | We consider general cyclic representations of the 6-vertex Yang-Baxter
algebra and analyze the associated quantum integrable systems, the
Bazhanov-Stroganov model and the corresponding chiral Potts model on finite
size lattices. We first determine the propagator operator in terms of the
chiral Potts transfer matrices and we compute the scalar product of separate
states (including the transfer matrix eigenstates) as a single determinant
formulae in the framework of Sklyanin's quantum separation of variables. Then,
we solve the quantum inverse problem and reconstruct the local operators in
terms of the separate variables. We also determine a basis of operators whose
form factors are characterized by a single determinant formulae. This implies
that the form factors of any local operator are expressed as finite sums of
determinants. Among these form factors written in determinant form are in
particular those which will reproduce the chiral Potts order parameters in the
thermodynamic limit.Comment: 45 page | On the form factors of local operators in the Bazhanov-Stroganov and
chiral Potts models | on the form factors of local operators in the bazhanov-stroganov and chiral potts models | cyclic representations baxter analyze integrable bazhanov stroganov chiral potts lattices. propagator chiral potts eigenstates determinant formulae sklyanin variables. solve reconstruct variables. determinant formulae. sums determinants. determinant reproduce chiral potts thermodynamic | non_dup | [] |
24945448 | 10.1007/s00023-014-0363-z | We give a complete framework for the Gupta-Bleuler quantization of the free
electromagnetic field on globally hyperbolic space-times. We describe
one-particle structures that give rise to states satisfying the microlocal
spectrum condition. The field algebras in the so-called Gupta-Bleuler
representations satisfy the time-slice axiom, and the corresponding vacuum
states satisfy the microlocal spectrum condition. We also give an explicit
construction of ground states on ultrastatic space-times. Unlike previous
constructions, our method does not require a spectral gap or the absence of
zero modes. The only requirement, the absence of zero-resonance states, is
shown to be stable under compact perturbations of topology and metric. Usual
deformation arguments based on the time-slice axiom then lead to a construction
of Gupta-Bleuler representations on a large class of globally hyperbolic
space-times. As usual, the field algebra is represented on an indefinite inner
product space, in which the physical states form a positive semi-definite
subspace. Gauge transformations are incorporated in such a way that the field
can be coupled perturbatively to a Dirac field. Our approach does not require
any topological restrictions on the underlying space-time.Comment: 28 pages, LaTeX, statement of Proposition 5.1 correcte | Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic
Space-Times | gupta-bleuler quantization of the maxwell field in globally hyperbolic space-times | gupta bleuler quantization electromagnetic globally hyperbolic times. satisfying microlocal condition. algebras gupta bleuler representations satisfy slice axiom satisfy microlocal condition. ultrastatic times. unlike constructions modes. requirement perturbations topology metric. usual deformation arguments slice axiom gupta bleuler representations globally hyperbolic times. usual indefinite definite subspace. transformations incorporated perturbatively dirac field. topological restrictions pages latex statement correcte | non_dup | [] |
25026942 | 10.1007/s00023-014-0366-9 | Random operators may acquire extended states formed from a multitude of
mutually resonating local quasi-modes. This mechanics is explored here in the
context of the random Schr\"odinger operator on the complete graph. The
operators exhibits local quasi modes mixed through a single channel. While most
of its spectrum consists of localized eigenfunctions, under appropriate
conditions it includes also bands of states which are delocalized in the
$\ell^1$-though not in $\ell^2$-sense, where the eigenvalues have the
statistics of \v{S}eba spectra. The analysis proceeds through some general
observations on the scaling limits of random functions in the Herglotz-Pick
class. The results are in agreement with a heuristic condition for the
emergence of resonant delocalization, which is stated in terms of the tunneling
amplitude among quasi-modes | Resonances and Partial Delocalization on the Complete Graph | resonances and partial delocalization on the complete graph | acquire multitude mutually resonating quasi modes. mechanics explored schr odinger graph. exhibits quasi channel. localized eigenfunctions delocalized eigenvalues spectra. proceeds herglotz pick class. heuristic emergence resonant delocalization stated tunneling quasi | non_dup | [] |
25002046 | 10.1007/s00023-014-0372-y | We provide a detailed analysis of the classical and quantized theory of a
multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime
metric and also to an external source term; thus the solutions form an affine
space. Following the formulation of affine field theories in terms of
presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171
(2014)], we determine the relative Cauchy evolution induced by metric as well
as source term perturbations and compute the automorphism group of natural
isomorphisms of the presymplectic vector space functor. Two pathological
features of this formulation are revealed: the automorphism group contains
elements that cannot be interpreted as global gauge transformations of the
theory; moreover, the presymplectic formulation does not respect a natural
requirement on composition of subsystems. We therefore propose a systematic
strategy to improve the original description of affine field theories at the
classical and quantized level, first passing to a Poisson algebra description
in the classical case. The idea is to consider state spaces on the classical
and quantum algebras suggested by the physics of the theory (in the classical
case, we use the affine solution space). The state spaces are not separating
for the algebras, indicating a redundancy in the description. Removing this
redundancy by a quotient, a functorial theory is obtained that is free of the
above mentioned pathologies. These techniques are applicable to general affine
field theories and Abelian gauge theories. The resulting quantized theory is
shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references
added. v3: 47 pages; compatible with version to appear in Annales Henri
Poincar | Locally covariant quantum field theory with external sources | locally covariant quantum field theory with external sources | quantized multiplet inhomogeneous klein gordon couple spacetime affine space. formulation affine presymplectic annales henri poincare cauchy perturbations automorphism isomorphisms presymplectic functor. pathological formulation automorphism interpreted transformations presymplectic formulation requirement subsystems. propose affine quantized passing poisson case. algebras affine separating algebras redundancy description. removing redundancy quotient functorial pathologies. applicable affine abelian theories. quantized dynamically pages deformation quantization added. pages compatible annales henri poincar | non_dup | [] |
25010985 | 10.1007/s00023-014-0373-x | We consider the question whether a static potential on an asymptotically flat
3-manifold can have nonempty zero set which extends to the infinity. We prove
that this does not occur if the metric is asymptotically Schwarzschild with
nonzero mass. If the asymptotic assumption is relaxed to the usual assumption
under which the total mass is defined, we prove that the static potential is
unique up to scaling unless the manifold is flat. We also provide some
discussion concerning the rigidity of complete asymptotically flat 3-manifolds
without boundary that admit a static potential.Comment: introduction revised; an outline of a space-time approach adde | Static potentials on asymptotically flat manifolds | static potentials on asymptotically flat manifolds | asymptotically manifold nonempty extends infinity. asymptotically schwarzschild nonzero mass. asymptotic relaxed usual unless manifold flat. concerning rigidity asymptotically manifolds admit revised outline adde | non_dup | [] |
25042461 | 10.1007/s00023-014-0378-5 | We show how to reduce the general formulation of the mass-angular
momentum-charge inequality, for axisymmetric initial data of the
Einstein-Maxwell equations, to the known maximal case whenever a geometrically
motivated system of equations admits a solution. It is also shown that the same
reduction argument applies to the basic inequality yielding a lower bound for
the area of black holes in terms of mass, angular momentum, and charge. This
extends previous work by the authors [4] (arXiv:1401.3384), in which the role
of charge was omitted. Lastly, we improve upon the hypotheses required for the
mass-angular momentum-charge inequality in the maximal case.Comment: 34 pages; final version. This article builds on previous work of the
authors (arXiv:1401.3384) by including the electromagnetic fiel | Deformations of Charged Axially Symmetric Initial Data and the
Mass-Angular Momentum-Charge Inequality | deformations of charged axially symmetric initial data and the mass-angular momentum-charge inequality | formulation inequality axisymmetric einstein maxwell maximal whenever geometrically motivated admits solution. argument applies inequality yielding holes charge. extends omitted. lastly hypotheses inequality maximal pages version. builds electromagnetic fiel | non_dup | [] |
44311594 | 10.1007/s00023-014-0379-4 | Given a unitary representation of a Lie group G on a Hilbert space H , we develop the theory of G-invariant self-adjoint extensions of symmetric operators using both von Neumann's theorem and the theory of quadratic forms. We also analyze the relation between the reduction theory of the unitary representation and the reduction of the G-invariant unbounded operator. We also prove a G-invariant version of the representation theorem for closed and semi-bounded quadratic forms. The previous results are applied to the study of G-invariant self-adjoint extensions of the Laplace&-Beltrami operator on a smooth Riemannian manifold with boundary on which the group G acts. These extensions are labeled by admissible unitaries U acting on the L 2-space at the boundary and having spectral gap at −1. It is shown that if the unitary representation V of the symmetry group G is traceable, then the self-adjoint extension of the Laplace&-Beltrami operator determined by U is G-invariant if U and V commute at the boundary. Various significant examples are discussed at the end.A. Ibort and J. M. Pérez-Pardo are partly supported by the project MTM2010-21186-C02-02 of the spanish Ministerio de Ciencia e Innovación and QUITEMAD programme P2009
ESP-1594. F. Lledó was partially supported by projects DGI MICIIN MTM2012-36372-C03-01 and Severo Ochoa SEV-2011-0087 of the spanish Ministry of Economy and Competition.
J. M. Pérez-Pardo was also partially supported in 2011 and 2012 by mobility grants of the “Universidad Carlos III de Madrid” | On Self-Adjoint Extensions and Symmetries in Quantum Mechanics | on self-adjoint extensions and symmetries in quantum mechanics | unitary hilbert adjoint extensions neumann quadratic forms. analyze unitary unbounded operator. quadratic forms. adjoint extensions laplace beltrami riemannian manifold acts. extensions labeled admissible unitaries acting unitary traceable adjoint laplace beltrami commute boundary. end.a. ibort pérez pardo partly spanish ministerio ciencia innovación quitemad programme lledó partially projects miciin severo ochoa spanish ministry economy competition. pérez pardo partially mobility grants “universidad carlos madrid” | non_dup | [] |
25043152 | 10.1007/s00023-014-0383-8 | We explore the possibility that the Higgs boson of the standard model be
actually a member of a larger family, by showing that a more elaborate internal
structure naturally arises from geometrical arguments, in the context of a
partly original handling of gauge fields which was put forward in previous
papers. A possible mechanism yielding the usual Higgs potential is proposed.
New types of point interactions, arising in particular from two-spinor index
contractions, are shown to be allowed.Comment: Corrected typos and added journal info, Annales Henri Poincar\'e
(2014). Springer link:
http://link.springer.com/article/10.1007/s00023-014-0383- | Natural extensions of electroweak geometry and Higgs interactions | natural extensions of electroweak geometry and higgs interactions | explore boson member elaborate naturally arises geometrical arguments partly handling papers. yielding usual proposed. arising spinor contractions corrected typos info annales henri poincar springer | non_dup | [] |
24981723 | 10.1007/s00023-014-0387-4 | In this article we discuss an exactly solvable, one-dimensional, periodic toy
charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103},
46002 (2013)]. In particular, driving the system with a uniform force, we show
that the depinning threshold configuration is an explicit function of the
underlying disorder, as is the evolution from the negative threshold to the
positive threshold, the latter admitting a description in terms of record
sequences. This evolution is described by an avalanche algorithm, which
identifies a sequence of static configurations that are stable at successively
stronger forcing, and is useful both for analysis and simulation. We focus in
particular on the behavior of the polarization $P$, which is related to the
cumulative avalanche size, as a function of the threshold force minus the
current force $(F_{\mathrm{th}} - F)$, as this has been the focus of several
prior numerical and analytical studies of CDW systems. The results presented
are rigorous, with exceptions explicitly indicated, and show that the depinning
transition in this model is indeed a dynamic critical phenomenon | Exact results for a toy model exhibiting dynamic criticality | exact results for a toy model exhibiting dynamic criticality | solvable d.c. kaspar mungan driving depinning disorder admitting record sequences. avalanche identifies configurations successively stronger forcing simulation. cumulative avalanche minus mathrm systems. rigorous exceptions explicitly depinning phenomenon | non_dup | [] |
52439537 | 10.1007/s00023-014-0388-3 | We study magnetic quantum Hall systems in a half-plane with Dirichlet boundary conditions along the edge. Much work has been done on the analysis of the currents associated with states whose energy is located between Landau levels. These edge states are localized near the boundary and they carry a non-zero current. In this article, we study the behavior of states with energy close to a Landau level that are referred to as bulk states in the physics literature. The magnetic Schrödinger operator is invariant with respect to translations in the direction of the edge and is a direct integral of operators indexed by a real wave number. We analyse the fiber operators and prove new asymptotics on the band functions and their first derivative as the wave number goes to infinity. We apply these results to prove that the current carried by a bulk state is small compared to the current carried by an edge state. We also prove that the bulk states are exponentially small near the edge | Characterization of bulk states in one-edge quantum Hall systems | characterization of bulk states in one-edge quantum hall systems | hall dirichlet edge. currents landau levels. localized carry current. landau referred literature. schrödinger translations indexed number. analyse fiber asymptotics goes infinity. state. exponentially | non_dup | [] |
24971835 | 10.1007/s00023-014-0389-2 | Two simple model operators are considered which have pre-existing resonances.
A potential corresponding to a small electric field, $f$, is then introduced
and the resonances of the resulting operator are considered as $f\to0$. It is
shown that these resonances are not continuous in this limit. It is conjectured
that a similar behavior will appear in more complicated models of atoms and
molecules. Numerical results are presented.Comment: 54 pages, 11 figures. No changes w.r.t. preprint version of
03/29/2014, except publisher information added. The final publication is
available at link.springer.co | Instability of pre-existing resonances under a small constant electric
field | instability of pre-existing resonances under a small constant electric field | resonances. resonances resonances limit. conjectured complicated molecules. pages figures. w.r.t. preprint publisher added. publication link.springer.co | non_dup | [] |
24987677 | 10.1007/s00023-014-0391-8 | To any solution of a linear system of differential equations, we associate a
kernel, correlators satisfying a set of loop equations, and in presence of
isomonodromic parameters, a Tau function. We then study their semiclassical
expansion (WKB type expansion in powers of the weight hbar per derivative) of
these quantities. When this expansion is of topological type (TT), the
coefficients of expansions are computed by the topological recursion with
initial data given by the semiclassical spectral curve of the linear system.
This provides an efficient algorithm to compute them at least when the
semiclassical spectral curve is of genus 0. TT is a non trivial property, and
it is an open problem to find a criterion which guarantees it is satisfied. We
prove TT and illustrate our construction for the linear systems associated to
the q-th reductions of KP - which contain the (p,q) models as a specialization.Comment: 49 page | Rational differential systems, loop equations, and application to the
q-th reductions of KP | rational differential systems, loop equations, and application to the q-th reductions of kp | associate kernel correlators satisfying isomonodromic function. semiclassical powers hbar quantities. topological expansions topological recursion semiclassical system. semiclassical genus trivial criterion guarantees satisfied. illustrate reductions | non_dup | [] |
25025045 | 10.1007/s00023-014-0394-5 | When a flux quantum is pushed through a gapped two-dimensional tight-binding
operator, there is an associated spectral flow through the gap which is shown
to be equal to the index of a Fredholm operator encoding the topology of the
Fermi projection. This is a natural mathematical formulation of Laughlin's
Gedankenexperiment. It is used to provide yet another proof of the bulk-edge
correspondence. Furthermore, when applied to systems with time reversal
symmetry, the spectral flow has a characteristic $Z_2$ signature, while for
particle-hole symmetric systems it leads to a criterion for the existence of
zero energy modes attached to half-flux tubes. Combined with other results,
this allows to explain all strong invariants of two-dimensional topological
insulators in terms of a single Fredholm operator.Comment: final version, to appear in Ann. H. Poincar | Spectral flows associated to flux tubes | spectral flows associated to flux tubes | pushed gapped tight fredholm encoding topology fermi projection. mathematical formulation laughlin gedankenexperiment. correspondence. reversal signature criterion attached tubes. invariants topological insulators fredholm ann. poincar | non_dup | [] |
25020628 | 10.1007/s00023-014-0395-4 | In this paper we extend our previous results concerning Jackson integral
solutions of the boundary quantum Knizhnik-Zamolodchikov equations with
diagonal K-operators to higher-spin representations of quantum affine
$\mathfrak{sl}_2$. First we give a systematic exposition of known results on
$R$-operators acting in the tensor product of evaluation representations in
Verma modules over quantum $\mathfrak{sl}_2$. We develop the corresponding
fusion of $K$-operators, which we use to construct diagonal $K$-operators in
these representations. We construct Jackson integral solutions of the
associated boundary quantum Knizhnik-Zamolodchikov equations and explain how in
the finite-dimensional case they can be obtained from our previous results by
the fusion procedure.Comment: 36 pages; some small additions and corrections concerning
mero-uniform convergence (Defn. 6.1) and rectified some notation issues for
the function \mathcal{Y} (p21 and onwards). appears in Annales Henri
Poincar\'e, 201 | Boundary quantum Knizhnik-Zamolodchikov equations and fusion | boundary quantum knizhnik-zamolodchikov equations and fusion | extend concerning jackson knizhnik zamolodchikov diagonal representations affine mathfrak exposition acting representations verma modules mathfrak fusion diagonal representations. jackson knizhnik zamolodchikov fusion pages additions concerning mero defn. rectified notation mathcal onwards annales henri poincar | non_dup | [] |
25046644 | 10.1007/s00023-015-0397-x | We propose a way to study one-dimensional statistical mechanics models with
complex-valued action using transfer operators. The argument consists of two
steps. First, the contour of integration is deformed so that the associated
transfer operator is a perturbation of a normal one. Then the transfer operator
is studied using methods of semi-classical analysis.
In this paper we concentrate on the second step, the main technical result
being a semi-classical estimate for powers of an integral operator which is
approximately normal.Comment: 28 pp, improved the presentatio | Semi-classical analysis of non self-adjoint transfer matrices in
statistical mechanics. I | semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. i | propose mechanics valued operators. argument steps. contour deformed perturbation one. analysis. concentrate powers presentatio | non_dup | [] |
25014067 | 10.1007/s00023-015-0398-9 | We consider the non-interacting source-free Maxwell field, described both in
terms of the vector potential and the field strength. Starting from the
classical field theory on contractible globally hyperbolic spacetimes, we
extend the classical field theory to general globally hyperbolic spacetimes in
two ways to obtain a "universal" theory and a "reduced" theory. The quantum
field theory in terms of the unital $*$-algebra of the smeared quantum field is
then obtained by an application of a suitable quantisation functor. We show
that the universal theories fail local covariance and dynamical locality owing
to the possibility of having non-trivial radicals in the classical and
non-trivial centres in the quantum case. The reduced theories are both locally
covariant and dynamically local. These models provide new examples relevant to
the discussion of how theories should be formulated so as to describe the same
physics in all spacetimes.Comment: 27pp v3: Some comments added; minor corrections and typos fixe | Dynamical locality of the free Maxwell field | dynamical locality of the free maxwell field | interacting maxwell strength. contractible globally hyperbolic spacetimes extend globally hyperbolic spacetimes ways universal theory. unital smeared quantisation functor. universal fail covariance locality owing trivial radicals trivial centres case. locally covariant dynamically local. formulated comments minor typos fixe | non_dup | [] |
43097275 | 10.1007/s00023-015-0399-8 | Author's manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-015-0399-8First available online: 14 February 2015In this work, we present an abstract framework that allows to obtain mixing (and in some cases sharp mixing) rates for a reasonable large class of invertible systems preserving an infinite measure. The examples explicitly considered are the invertible analogue of both Markov and non-Markov unit interval maps. For these examples, in addition to optimal results on mixing and rates of mixing in the infinite case, we obtain results on the decay of correlation in the finite case of invertible non-Markov maps, which, to our knowledge, were not previously addressed. The proposed method consists of a combination of the framework of operator renewal theory, as introduced in the context of dynamical systems by Sarig (Invent Math 150:629–653, 2002), with the framework of function spaces of distributions developed in the recent years along the lines of Blank et al. (Nonlinearity 15:1905–1973, 2001).European Research Council (ERC | Mixing for some non-uniformly hyperbolic systems | mixing for some non-uniformly hyperbolic systems | manuscript. publication springer february sharp reasonable invertible preserving infinite measure. explicitly invertible analogue markov markov maps. infinite invertible markov addressed. renewal sarig invent math blank nonlinearity .european council | non_dup | [] |
25047916 | 10.1007/s00023-015-0400-6 | We consider a real periodic Schr\"odinger operator and a physically relevant
family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the
spectrum, and we investigate the localization properties of the corresponding
composite Wannier functions. To this aim, we show that in dimension $d \leq 3$
there exists a global frame consisting of smooth quasi-Bloch functions which
are both periodic and time-reversal symmetric. Aiming to applications in
computational physics, we provide a constructive algorithm to obtain such a
Bloch frame. The construction yields the existence of a basis of composite
Wannier functions which are real-valued and almost-exponentially localized.
The proof of the main result exploits only the fundamental symmetries of the
projector on the relevant bands, allowing applications, beyond the model
specified above, to a broad range of gapped periodic quantum systems with a
time-reversal symmetry of bosonic type.Comment: 40 pages, 3 figures. Minor corrections implemented, some references
added. To appear in Annales Henri Poicar\' | Construction of real-valued localized composite Wannier functions for
insulators | construction of real-valued localized composite wannier functions for insulators | schr odinger physically bloch separated localization composite wannier functions. consisting quasi bloch reversal symmetric. aiming constructive bloch frame. composite wannier valued exponentially localized. exploits symmetries projector allowing specified broad gapped reversal bosonic pages figures. minor implemented added. annales henri poicar | non_dup | [] |
24966686 | 10.1007/s00023-015-0401-5 | In 1969, Choquet-Bruhat and Geroch established the existence of a unique
maximal globally hyperbolic Cauchy development of given initial data for the
Einstein equations. Their proof, however, has the unsatisfactory feature that
it relies crucially on the axiom of choice in the form of Zorn's lemma. In this
paper we present a proof that avoids the use of Zorn's lemma. In particular, we
provide an explicit construction of this maximal globally hyperbolic
development.Comment: 25 pages, 6 figures, v2 small changes and minor correction, v3
version accepted for publicatio | On the Existence of a Maximal Cauchy Development for the Einstein
Equations - a Dezornification | on the existence of a maximal cauchy development for the einstein equations - a dezornification | choquet bruhat geroch maximal globally hyperbolic cauchy einstein equations. unsatisfactory relies crucially axiom zorn lemma. avoids zorn lemma. maximal globally hyperbolic pages minor publicatio | non_dup | [] |
25038332 | 10.1007/s00023-015-0418-9 | We present a rigorous and fully consistent $K$-theoretic framework for
studying gapped topological phases of free fermions such as topological
insulators. It utilises and profits from powerful techniques in operator
$K$-theory. From the point of view of symmetries, especially those of time
reversal, charge conjugation, and magnetic translations, operator $K$-theory is
more general and natural than the commutative topological theory. Our approach
is model-independent, and only the symmetry data of the dynamics, which may
include information about disorder, is required. This data is completely
encoded in a suitable $C^*$-superalgebra. From a representation-theoretic point
of view, symmetry-compatible gapped phases are classified by the
super-representation group of this symmetry algebra. Contrary to existing
literature, we do not use $K$-theory to classify phases in an absolute sense,
but only relative to some arbitrary reference. $K$-theory groups are better
thought of as groups of obstructions between homotopy classes of gapped phases.
Besides rectifying various inconsistencies in the existing literature on
$K$-theory classification schemes, our treatment has conceptual simplicity in
its treatment of all symmetries equally. The Periodic Table of Kitaev is
exhibited as a special case within our framework, and we prove that the
phenomena of periodicity and dimension shifts are robust against disorder and
magnetic fields.Comment: 41 pages, revised version with a new abstract, introductory sections
and critique of the literatur | On the K-theoretic classification of topological phases of matter | on the k-theoretic classification of topological phases of matter | rigorous theoretic studying gapped topological fermions topological insulators. utilises profits powerful theory. symmetries reversal conjugation translations commutative topological theory. disorder required. encoded superalgebra. theoretic compatible gapped classified super algebra. contrary classify reference. thought obstructions homotopy gapped phases. besides rectifying inconsistencies schemes conceptual simplicity symmetries equally. kitaev exhibited phenomena periodicity shifts robust disorder pages revised introductory critique literatur | non_dup | [] |
25002897 | 10.1007/s00023-015-0420-2 | In this sequel paper we give a shorter, second proof of the monotonicity of
the Hawking mass for time flat surfaces under spacelike uniformly area
expanding flows in spacetimes that satisfy the dominant energy condition. We
also include a third proof which builds on a known formula and describe a class
of sufficient conditions of divergence type for the monotonicity of the Hawking
mass. These flows of surfaces may have connections to the problem in general
relativity of bounding the total mass of a spacetime from below by the
quasi-local mass of spacelike 2-surfaces in the spacetime.Comment: 19 pages, 1 figur | Time flat surfaces and the monotonicity of the spacetime Hawking mass II | time flat surfaces and the monotonicity of the spacetime hawking mass ii | sequel shorter monotonicity hawking spacelike uniformly expanding flows spacetimes satisfy condition. builds divergence monotonicity hawking mass. flows connections relativity bounding spacetime quasi spacelike pages figur | non_dup | [] |
29509855 | 10.1007/s00023-015-0422-0 | We propose a new family of matrix models whose 1/N expansion captures the
all-genus topological string on toric Calabi-Yau threefolds. These matrix
models are constructed from the trace class operators appearing in the
quantization of the corresponding mirror curves. The fact that they provide a
non-perturbative realization of the (standard) topological string follows from
a recent conjecture connecting the spectral properties of these operators, to
the enumerative invariants of the underlying Calabi-Yau threefolds. We study in
detail the resulting matrix models for some simple geometries, like local P^2
and local F_2, and we verify that their weak 't Hooft coupling expansion
reproduces the topological string free energies near the conifold singularity.
These matrix models are formally similar to those appearing in the Fermi-gas
formulation of Chern-Simons-matter theories, and their 1/N expansion receives
non-perturbative corrections determined by the Nekrasov-Shatashvili limit of
the refined topological string.Comment: 30 pages, 6 figures; v2 : typos corrected, comments adde | Matrix models from operators and topological strings | matrix models from operators and topological strings | propose captures genus topological toric calabi threefolds. trace appearing quantization mirror curves. perturbative realization topological conjecture connecting enumerative invariants calabi threefolds. geometries verify hooft reproduces topological conifold singularity. formally appearing fermi formulation chern simons receives perturbative nekrasov shatashvili refined topological pages typos corrected comments adde | non_dup | [] |
24965737 | 10.1007/s00023-015-0423-z | We prove a formula for the global gravitational anomaly of the self-dual
field theory in the presence of background gauge fields, assuming the results
of arXiv:1110.4639. Along the way, we also clarify various points about the
self-dual field theory. In particular, we give a general definition of the
theta characteristic entering its partition function and settle the issue of
its possible metric dependence. We treat the cohomological version of type IIB
supergravity as an example of the formalism: a mixed gauge-gravitational global
anomaly, occurring when the B-field and Ramond-Ramond 2-form gauge fields have
non-trivial Wilson lines, cancels provided a certain cobordism group vanishes.Comment: 38 pages. v3: Corrections in the discussion of the global anomaly
cancellation in type IIB sugra. Typos correcte | The global anomaly of the self-dual field in general backgrounds | the global anomaly of the self-dual field in general backgrounds | gravitational anomaly clarify theory. theta entering partition settle dependence. treat cohomological supergravity formalism gravitational anomaly occurring ramond ramond trivial wilson cancels cobordism pages. anomaly cancellation sugra. typos correcte | non_dup | [] |
42637804 | 10.1007/s00023-015-0428-7 | The initial-value problem for the drift-diffusion equation arising from the
model of semiconductor device simulations is studied. The dissipation on this
equation is given by the fractional Laplacian. When the exponent of the
fractional Laplacian is large, large-time behavior of solutions is known.
However, when the exponent is small, the perturbation methods used in the
preceding works would not work. Large-time behavior of solutions to the
drift-diffusion equation with small exponent is discussed. Particularly, the
asymptotic expansion of solutions with high-order is derived | Asymptotic expansion of solutions to the drift-diffusion equation with
fractional dissipation | asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation | drift arising semiconductor studied. dissipation fractional laplacian. exponent fractional laplacian known. exponent perturbation preceding work. drift exponent discussed. asymptotic | non_dup | [] |
29506243 | 10.1007/s00023-015-0433-x | The divisible sandpile starts with i.i.d. random variables ("masses") at the
vertices of an infinite, vertex-transitive graph, and redistributes mass by a
local toppling rule in an attempt to make all masses at most 1. The process
stabilizes almost surely if m<1 and it almost surely does not stabilize if m>1,
where $m$ is the mean mass per vertex. The main result of this paper is that in
the critical case m=1, if the initial masses have finite variance, then the
process almost surely does not stabilize. To give quantitative estimates on a
finite graph, we relate the number of topplings to a discrete biLaplacian
Gaussian field.Comment: 34 pages, to appear in Annales Henri Poincar | The divisible sandpile at critical density | the divisible sandpile at critical density | divisible sandpile starts i.i.d. infinite transitive redistributes toppling attempt stabilizes surely surely stabilize vertex. surely stabilize. relate topplings bilaplacian pages annales henri poincar | non_dup | [] |
29504544 | 10.1007/s00023-015-0438-5 | We define the (total) center of mass for suitably asymptotically hyperbolic
time-slices of asymptotically anti-de Sitter spacetimes in general relativity.
We do so in analogy to the picture that has been consolidated for the (total)
center of mass of suitably asymptotically Euclidean time-slices of
asymptotically Minkowskian spacetimes (isolated systems). In particular, we
unite -- an altered version of -- the approach based on Hamiltonian charges
with an approach based on CMC-foliations near infinity. The newly defined
center of mass transforms appropriately under changes of the asymptotic
coordinates and evolves in the direction of an appropriately defined linear
momentum under the Einstein evolution equations | On the center of mass of asymptotically hyperbolic initial data sets | on the center of mass of asymptotically hyperbolic initial data sets | suitably asymptotically hyperbolic slices asymptotically sitter spacetimes relativity. analogy picture consolidated suitably asymptotically euclidean slices asymptotically minkowskian spacetimes unite altered charges foliations infinity. newly transforms appropriately asymptotic evolves appropriately einstein | non_dup | [] |
29503223 | 10.1007/s00023-015-0441-x | We consider a finite region of a $d$-dimensional lattice, $d\in\mathbb{N}$,
of weakly coupled harmonic oscillators. The coupling is provided by a
nearest-neighbour potential (harmonic or not) of size $\varepsilon$. Each
oscillator weakly interacts by force of order $\varepsilon$ with its own
stochastic Langevin thermostat of arbitrary positive temperature. We
investigate limiting as $\varepsilon\rightarrow 0$ behaviour of solutions of
the system and of the local energy of oscillators on long-time intervals of
order $\varepsilon^{-1}$ and in a stationary regime. We show that it is
governed by an effective equation which is a dissipative SDE with nondegenerate
diffusion. Next we assume that the interaction potential is of size
$\varepsilon\lambda$, where $\lambda$ is another small parameter, independent
from $\varepsilon$. Solutions corresponding to this scaling describe small low
temperature oscillations. We prove that in a stationary regime, under the limit
$\varepsilon\rightarrow 0$, the main order in $\lambda$ of the averaged
Hamiltonian energy flow is proportional to the gradient of temperature. We show
that the coefficient of proportionality, which we call the conductivity, admits
a representation through stationary space-time correlations of the energy flow.
Most of the results and convergences we obtain are uniform with respect to the
number of oscillators in the system.Comment: 52 page | Nonequilibrium statistical mechanics of weakly stochastically perturbed
system of oscillators | nonequilibrium statistical mechanics of weakly stochastically perturbed system of oscillators | mathbb weakly harmonic oscillators. nearest neighbour harmonic varepsilon oscillator weakly interacts varepsilon stochastic langevin thermostat temperature. limiting varepsilon rightarrow oscillators intervals varepsilon stationary regime. governed dissipative nondegenerate diffusion. varepsilon lambda lambda varepsilon oscillations. stationary varepsilon rightarrow lambda averaged temperature. proportionality call conductivity admits stationary flow. convergences oscillators | non_dup | [] |
52428828 | 10.1007/s00023-015-0442-9 | International audienceWe study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law distribution function, almost surely in the random environment and in the full range of time scales and temperatures for which such a result can be expected to hold. This establishes that the dynamics ages in the same way as Bouchaud's REM-like trap model, thus extending the universality class of the latter model. The proof relies on a clock process convergence result of a new type where the number of summands is itself a clock process. This reflects the fact that the exploration process of Metropolis dynamics is itself an aging process, governed by its own clock. Both clock processes are shown to converge to stable subor-dinators below certain critical lines in their timescale and temperature domains, almost surely in the random environment | Convergence of Clock Processes and Aging in Metropolis Dynamics of a Truncated REM | convergence of clock processes and aging in metropolis dynamics of a truncated rem | audiencewe aging truncated evolving metropolis dynamics. overlap converges arcsine surely hold. establishes ages bouchaud trap extending universality model. relies clock summands clock process. reflects exploration metropolis aging governed clock. clock converge subor dinators timescale surely | non_dup | [] |
25030722 | 10.1007/s00023-015-0446-5 | In this paper, we introduce new methods for solving the vacuum Einstein
constraints equations: the first one is based on Schaefer's fixed point theorem
(known methods use Schauder's fixed point theorem) while the second one uses
the concept of half-continuity coupled with the introduction of local
supersolutions. These methods allow to: unify some recent existence results,
simplify many proofs (for instance, the main theorem in arXiv:1012.2188) and
weaken the assumptions of many recent results.Comment: In this version, I change from 3-dimensional case to n-dimensional
cas | Applications of Fixed Point Theorems to the Vacuum Einstein Constraint
Equations with Non-Constant Mean Curvature | applications of fixed point theorems to the vacuum einstein constraint equations with non-constant mean curvature | solving einstein schaefer schauder continuity supersolutions. unify simplify proofs weaken assumptions | non_dup | [] |
29509173 | 10.1007/s00023-015-0453-6 | We study inverse scattering problems at a fixed energy for radial
Schr\"{o}dinger operators on $\R^n$, $n \geq 2$. First, we consider the class
$\mathcal{A}$ of potentials $q(r)$ which can be extended analytically in $\Re z
\geq 0$ such that $\mid q(z)\mid \leq C \ (1+ \mid z \mid )^{-\rho}$, $\rho
\textgreater{} \frac{3}{2}$. If $q$ and $\tilde{q}$ are two such potentials and
if the corresponding phase shifts $\delta\_l$ and $\tilde{\delta}\_l$ are
super-exponentially close, then $q=\tilde{q}$. Secondly, we study the class of
potentials $q(r)$ which can be split into $q(r)=q\_1(r) + q\_2(r)$ such that
$q\_1(r)$ has compact support and $q\_2 (r) \in \mathcal{A}$. If $q$ and
$\tilde{q}$ are two such potentials, we show that for any fixed
$a\textgreater{}0$, ${\ds{\delta\_l - \tilde{\delta}\_l \ = \ o \left(
\frac{1}{l^{n-3}} \ \left( {\frac{ae}{2l}}\right)^{2l}\right)}}$ when $l
\rightarrow +\infty$ if and only if $q(r)=\tilde{q}(r)$ for almost all $r \geq
a$. The proofs are close in spirit with the celebrated Borg-Marchenko
uniqueness theorem, and rely heavily on the localization of the Regge poles
that could be defined as the resonances in the complexified angular momentum
plane. We show that for a non-zero super-exponentially decreasing potential,
the number of Regge poles is always infinite and moreover, the Regge poles are
not contained in any vertical strip in the right-half plane. For potentials
with compact support, we are able to give explicitly their asymptotics. At
last, for potentials which can be extended analytically in $\Re z \geq 0$ with
$\mid q(z)\mid \leq C \ (1+ \mid z \mid )^{-\rho}$, $\rho \textgreater{}1$ , we
show that the Regge poles are confined in a vertical strip in the complex
plane.Comment: 52 page | Local inverse scattering at a fixed energy for radial Schr{\"o}dinger
operators and localization of the Regge poles | local inverse scattering at a fixed energy for radial schr{\"o}dinger operators and localization of the regge poles | schr dinger mathcal potentials analytically textgreater frac tilde potentials shifts delta tilde delta super exponentially tilde secondly potentials split mathcal tilde potentials textgreater delta tilde delta frac frac rightarrow infty tilde proofs spirit celebrated borg marchenko uniqueness rely heavily localization regge poles resonances complexified plane. super exponentially decreasing regge poles infinite regge poles strip plane. potentials explicitly asymptotics. potentials analytically textgreater regge poles confined strip | non_dup | [] |
29543733 | 10.1007/s00023-015-0455-4 | We present a generalization of Minkowski's classic theorem on the
reconstruction of tetrahedra from algebraic data to homogeneously curved
spaces. Euclidean notions such as the normal vector to a face are replaced by
Levi-Civita holonomies around each of the tetrahedron's faces. This allows the
reconstruction of both spherical and hyperbolic tetrahedra within a unified
framework. A new type of hyperbolic simplex is introduced in order for all the
sectors encoded in the algebraic data to be covered. Generalizing the phase
space of shapes associated to flat tetrahedra leads to group valued moment maps
and quasi-Poisson spaces. These discrete geometries provide a natural arena for
considering the quantization of gravity including a cosmological constant. A
concrete realization of this is provided by the relation with the spin-network
states of loop quantum gravity. This work therefore provides a bottom-up
justification for the emergence of deformed gauge symmetries and quantum groups
in 3+1 dimensional covariant loop quantum gravity in the presence of a
cosmological constant.Comment: 38 pages and 9 figure | Encoding Curved Tetrahedra in Face Holonomies: a Phase Space of Shapes
from Group-Valued Moment Maps | encoding curved tetrahedra in face holonomies: a phase space of shapes from group-valued moment maps | generalization minkowski classic reconstruction tetrahedra algebraic homogeneously curved spaces. euclidean notions replaced levi civita holonomies tetrahedron faces. reconstruction spherical hyperbolic tetrahedra unified framework. hyperbolic simplex sectors encoded algebraic covered. generalizing shapes tetrahedra valued moment quasi poisson spaces. geometries arena quantization cosmological constant. concrete realization gravity. justification emergence deformed symmetries covariant cosmological pages | non_dup | [] |
29503272 | 10.1007/s00023-015-0456-3 | We show that the Anderson model has a transition from localization to
delocalization at exactly 2 dimensional growth rate on antitrees with
normalized edge weights which are certain discrete graphs. The kinetic part has
a one-dimensional structure allowing a description through transfer matrices
which involve some Schur complement. For such operators we introduce the notion
of having one propagating channel and extend theorems from the theory of
one-dimensional Jacobi operators that relate the behavior of transfer matrices
with the spectrum. These theorems are then applied to the considered model. In
essence, in a certain energy region the kinetic part averages the random
potentials along shells and the transfer matrices behave similar as for a
one-dimensional operator with random potential of decaying variance. At $d$
dimensional growth for $d>2$ this effective decay is strong enough to obtain
absolutely continuous spectrum, whereas for some uniform $d$ dimensional growth
with $d<2$ one has pure point spectrum in this energy region. At exactly
uniform $2$ dimensional growth also some singular continuous spectrum appears,
at least at small disorder. As a corollary we also obtain a change from
singular spectrum ($d\leq 2$) to absolutely continuous spectrum ($d\geq 3)$ for
random operators of the type $\mathcal{P}_r \Delta_d \mathcal{P}_r+\lambda
\mathcal{V}$ on $\mathbb{Z}^d$, where $\mathcal{P}_r$ is an orthogonal radial
projection, $\Delta_d$ the discrete adjacency operator (Laplacian) on
$\mathbb{Z}^d$ and $\lambda \mathcal{V}$ a random potential.Comment: 38 pages, 1 figure; Introduction reorganized, Corollary 1.3 added and
almost sure essential spectrum now characterized (Proposition 1.4 | Anderson transition at 2 dimensional growth rate on antitrees and
spectral theory for operators with one propagating channel | anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel | anderson localization delocalization antitrees weights graphs. allowing involve schur complement. notion propagating extend theorems jacobi relate spectrum. theorems model. essence averages potentials shells behave decaying variance. absolutely region. singular disorder. corollary singular absolutely mathcal delta mathcal lambda mathcal mathbb mathcal orthogonal projection delta adjacency laplacian mathbb lambda mathcal pages reorganized corollary sure | non_dup | [] |
29535014 | 10.1007/s00023-016-0458-9 | We obtain a reduction scheme for the study of the quantum evolution of an
atom in constant magnetic fields using the method developed by Martinez, Nenciu
and Sordoni based on the construction of almost invariant subspace. In
Martinez-Sordoni \cite{MaSo2} such a case is also studied but their reduced
Hamiltonian includes the vector potential terms. In this paper, using the
center of mass coordinates and constructing the almost invariant subspace
different from theirs, we obtain the reduced Hamiltonian which does not include
the vector potential terms. Using the reduced evolution we also obtain the
asymptotic expantion of the evolution for a specific localized initial data,
which verifies the straight motion of an atom in constatnt magnetic fields | Born-Oppenheimer approximation for an atom in constant magnetic fields | born-oppenheimer approximation for an atom in constant magnetic fields | atom martinez nenciu sordoni subspace. martinez sordoni cite maso terms. constructing subspace terms. asymptotic expantion localized verifies straight atom constatnt | non_dup | [] |
29526103 | 10.1007/s00023-016-0460-2 | We consider the problem of finding universal bounds of "isoperimetric" or
"isodiametric" type on the spectral gap of the Laplacian on a metric graph with
natural boundary conditions at the vertices, in terms of various analytical and
combinatorial properties of the graph: its total length, diameter, number of
vertices and number of edges. We investigate which combinations of parameters
are necessary to obtain non-trivial upper and lower bounds and obtain a number
of sharp estimates in terms of these parameters. We also show that, in contrast
to the Laplacian matrix on a combinatorial graph, no bound depending only on
the diameter is possible. As a special case of our results on metric graphs, we
deduce estimates for the normalised Laplacian matrix on combinatorial graphs
which, surprisingly, are sometimes sharper than the ones obtained by purely
combinatorial methods in the graph theoretical literature | On the Spectral Gap of a Quantum Graph | on the spectral gap of a quantum graph | universal bounds isoperimetric isodiametric laplacian combinatorial edges. combinations trivial bounds sharp parameters. laplacian combinatorial possible. deduce normalised laplacian combinatorial surprisingly sometimes sharper purely combinatorial | non_dup | [] |
25018480 | 10.1007/s00023-016-0462-0 | We study the spectral properties of the Sturm Hamiltolian of eventually
constant type, which includes the Fibonacci Hamiltonian. Let $s$ be the
Hausdorff dimension of the spectrum. For $V>20$, we show that the restriction
of the $s$-dimensional Hausdorff measure to the spectrum is a Gibbs type
measure; the density of states measure is a Markov measure. Based on the fine
structures of these measures, we show that both measures are exact dimensional;
we obtain exact asymptotic behaviors for the optimal H\"older exponent and the
Hausdorff dimension of the density of states measure and for the Hausdorff
dimension of the spectrum. As a consequence, if the frequency is not silver
number type, then for $V$ big enough, we establish strict inequalities between
these three spectral characteristics.
We achieve them by introducing an auxiliary symbolic dynamical system and
applying the thermodynamical and multifractal formalisms of almost additive
potentials.Comment: This is a revised version. We generalize the results for all the
frequencies of eventurally constant type. Accepted by Annales Henri Poincar | The spectral properties of the strongly coupled Sturm Hamiltonian of
eventually constant type | the spectral properties of the strongly coupled sturm hamiltonian of eventually constant type | sturm hamiltolian eventually fibonacci hamiltonian. hausdorff spectrum. restriction hausdorff gibbs markov measure. fine asymptotic behaviors older exponent hausdorff hausdorff spectrum. silver establish strict inequalities characteristics. introducing auxiliary symbolic thermodynamical multifractal formalisms additive revised version. generalize eventurally type. annales henri poincar | non_dup | [] |
29521866 | 10.1007/s00023-016-0463-z | We present a definition of indefinite Kasparov modules, a generalisation of
unbounded Kasparov modules modelling non-symmetric and non-elliptic (e.g.
hyperbolic) operators. Our main theorem shows that to each indefinite Kasparov
module we can associate a pair of (genuine) Kasparov modules, and that this
process is reversible. We present three examples of our framework: the Dirac
operator on a pseudo-Riemannian spin manifold (i.e. a manifold with an
indefinite metric), the harmonic oscillator, and the construction via the
Kasparov product of an indefinite spectral triple from a family of spectral
triples. This last construction corresponds to a foliation of a globally
hyperbolic spacetime by spacelike hypersurfaces.Comment: 24 pages, Annales Henri Poincar\'e, online version 201 | Indefinite Kasparov modules and pseudo-Riemannian manifolds | indefinite kasparov modules and pseudo-riemannian manifolds | indefinite kasparov modules generalisation unbounded kasparov modules elliptic e.g. hyperbolic operators. indefinite kasparov module associate genuine kasparov modules reversible. dirac pseudo riemannian manifold i.e. manifold indefinite harmonic oscillator kasparov indefinite triple triples. foliation globally hyperbolic spacetime spacelike pages annales henri poincar | non_dup | [] |
29505488 | 10.1007/s00023-016-0465-x | We study random Hamiltonians on finite-size cubes and waveguide segments of
increasing diameter. The number of random parameters determining the operator
is proportional to the volume of the cube. In the asymptotic regime where the
cube size, and consequently the number of parameters as well, tends to
infinity, we derive deterministic and probabilistic variational bounds on the
lowest eigenvalue, i.e. the spectral minimum, as well as exponential
off-diagonal decay of the Green function at energies above, but close to the
overall spectral bottom | Quantum Hamiltonians with weak random abstract perturbation. I. Initial
length scale estimate | quantum hamiltonians with weak random abstract perturbation. i. initial length scale estimate | hamiltonians cubes waveguide segments diameter. determining cube. asymptotic cube tends infinity derive deterministic probabilistic variational bounds eigenvalue i.e. exponential diagonal | non_dup | [] |
29541770 | 10.1007/s00023-016-0466-9 | We analyze spin-0 relativistic scattering of charged particles propagating in
the exterior, $\Lambda \subset \mathbb{R}^3$, of a compact obstacle $K \subset
\mathbb{R}^3$. The connected components of the obstacle are handlebodies. The
particles interact with an electro-magnetic field in $\Lambda$ and an
inaccessible magnetic field localized in the interior of the obstacle (through
the Aharonov-Bohm effect). We obtain high-momenta estimates, with error bounds,
for the scattering operator that we use to recover physical information: We
give a reconstruction method for the electric potential and the exterior
magnetic field and prove that, if the electric potential vanishes, circulations
of the magnetic potential around handles (or equivalently, by Stokes' theorem,
magnetic fluxes over transverse sections of handles) of the obstacle can be
recovered, modulo $2 \pi$. We additionally give a simple formula for the
high-momenta limit of the scattering operator in terms of certain magnetic
fluxes, in the absence of electric potential. If the electric potential does
not vanish, the magnetic fluxes on the handles above referred can be only
recovered modulo $\pi$ and the simple expression of the high-momenta limit of
the scattering operator does not hold true | Aharonov-Bohm Effect and High-Momenta Inverse Scattering for the
Klein-Gordon Equation | aharonov-bohm effect and high-momenta inverse scattering for the klein-gordon equation | analyze relativistic propagating exterior lambda mathbb obstacle mathbb obstacle handlebodies. interact electro lambda inaccessible localized interior obstacle aharonov bohm momenta bounds recover reconstruction exterior vanishes circulations handles equivalently stokes fluxes handles obstacle recovered modulo additionally momenta fluxes potential. vanish fluxes handles referred recovered modulo momenta hold | non_dup | [] |
29556497 | 10.1007/s00023-016-0467-8 | One manifestation of quantum resonances is a large sojourn time, or
autocorrelation, for states which are initially localized. We elaborate on
Lavine's time-energy uncertainty principle and give an estimate on the sojourn
time. For the case of perturbed embedded eigenstates the bound is explicit and
involves Fermi's Golden Rule. It is valid for a very general class of systems.
We illustrate the theory by applications to resonances for time dependent
systems including the AC Stark effect as well as multistate systems.Comment: Version to appear in Annales Henri Poincar\' | Energy-time uncertainty principle and lower bounds on sojourn time | energy-time uncertainty principle and lower bounds on sojourn time | manifestation resonances sojourn autocorrelation initially localized. elaborate lavine sojourn time. perturbed embedded eigenstates involves fermi golden rule. valid systems. illustrate resonances stark multistate annales henri poincar | non_dup | [] |