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2526121 | 10.1007/s00023-005-0219-7 | Casimir effect, in a broad interpretation which we adopt here, consists in a
backreaction of a quantum system to adiabatically changing external conditions.
Although the system is usually taken to be a quantum field, we show that this
restriction rather blurs than helps to clarify the statement of the problem. We
discuss the problem from the point of view of algebraic structure of quantum
theory, which is most appropriate in this context. The system in question may
be any quantum system, among others both finite as infinite dimensional
canonical systems are allowed. A simple finite-dimensional model is discussed.
We identify precisely the source of difficulties and infinities in most of
traditional treatments of the problem for infinite dimensional systems (such as
quantum fields), which is incompatibility of algebras of observables or their
representations. We formulate conditions on model idealizations which are
acceptable for the discussion of the adiabatic backreaction problem. In the
case of quantum field models in that class we find that the normal ordered
energy density is a well defined distribution, yielding global energy in the
limit of a unit test function. Although we see the "zero point" expressions as
inappropriate, we show how they can arise in the quantum field theory context
as a result of uncontrollable manipulations.Comment: 40 pages, AMS-LaTeX; to appear in Ann. H. Poincar | Quantum backreaction (Casimir) effect I. What are admissible
idealizations? | quantum backreaction (casimir) effect i. what are admissible idealizations? | casimir broad adopt backreaction adiabatically changing conditions. restriction blurs helps clarify statement problem. algebraic context. infinite canonical allowed. discussed. precisely difficulties infinities traditional treatments infinite incompatibility algebras observables representations. formulate idealizations acceptable adiabatic backreaction problem. ordered yielding function. expressions inappropriate arise uncontrollable pages latex ann. poincar | non_dup | [] |
2526049 | 10.1007/s00023-005-0226-8 | The universal covering of SO(3) is modelled as a reflection group G_R in a
representation independent fashion. For relativistic quantum fields, the Unruh
effect of vacuum states is known to imply an intrinsic form of reflection
symmetry, which is referred to as "modular P_1CT-symmetry (Bisognano, Wichmann,
1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to
construct a representation of G_R by pairs of modular P_1CT-operators. The
representation thus obtained satisfies Pauli's spin-statistics relation.Comment: Accepted for publication in Ann. H. Poincare, (annoying) misprints
correcte | Spin, Statistics, and Reflections, I. Rotation Invariance | spin, statistics, and reflections, i. rotation invariance | universal covering modelled reflection fashion. relativistic unruh imply intrinsic reflection referred modular bisognano wichmann guido longo funct modular operators. satisfies pauli publication ann. poincare annoying misprints correcte | non_dup | [] |
2556096 | 10.1007/s00023-005-0229-5 | We prove the property of stochastic stability previously introduced as a
consequence of the (unproved) continuity hypothesis in the temperature of the
spin-glass quenched state. We show that stochastic stability holds in
beta-average for both the Sherrington-Kirkpatrick model in terms of the square
of the overlap function and for the Edwards-Anderson model in terms of the bond
overlap. We show that the volume rate at which the property is reached in the
thermodynamic limit is V^{-1}. As a byproduct we show that the stochastic
stability identities coincide with those obtained with a different method by
Ghirlanda and Guerra when applyed to the thermal fluctuations only.Comment: 12 pages, revised versio | Spin-Glass Stochastic Stability: a Rigorous Proof | spin-glass stochastic stability: a rigorous proof | stochastic unproved continuity glass quenched state. stochastic beta sherrington kirkpatrick overlap edwards anderson bond overlap. reached thermodynamic byproduct stochastic identities coincide ghirlanda guerra applyed pages revised versio | non_dup | [] |
2555990 | 10.1007/s00023-005-0231-y | We study non--adiabatic transitions in scattering theory for the time
dependent molecular Schroedinger equation in the Born--Oppenheimer limit. We
assume the electron Hamiltonian has finitely many levels and consider the
propagation of coherent states with high enough total energy. When two of the
electronic levels are isolated from the rest of the electron Hamiltonian's
spectrum and display an avoided crossing, we compute the component of the
nuclear wave function associated with the non--adiabatic transition that is
generated by propagation through the avoided crossing. This component is shown
to be exponentially small in the square of the Born--Oppenheimer parameter, due
to the Landau-Zener mechanism. It propagates asymptotically as a free Gaussian
in the nuclear variables, and its momentum is shifted. The total transition
probability for this transition and the momentum shift are both larger than
what one would expect from a naive approximation and energy conservation | Determination of Non-Adiabatic Scattering Wave Functions in a
Born-Oppenheimer Model | determination of non-adiabatic scattering wave functions in a born-oppenheimer model | adiabatic schroedinger born oppenheimer limit. finitely propagation coherent energy. display avoided crossing adiabatic propagation avoided crossing. exponentially born oppenheimer landau zener mechanism. propagates asymptotically shifted. naive conservation | non_dup | [] |
2526222 | 10.1007/s00023-005-0232-x | We work out the general features of perturbative field theory on
noncommutative manifolds defined by isospectral deformation. These (in general
curved) `quantum spaces', generalizing Moyal planes and noncommutative tori,
are constructed using Rieffel's theory of deformation quantization for action
of $\R^l$. Our framework, incorporating background field methods and tools of
QFT in curved spaces, allows to deal both with compact and non-compact spaces,
as well as with periodic or not deformations, essentially in the same way. We
compute the quantum effective action up to one loop for a scalar theory,
showing the different UV/IR mixing phenomena for different kinds of isospectral
deformations. The presence and behavior of the non-planar parts of the Green
functions is understood simply in terms of off-diagonal heat kernel
contributions. For periodic deformations, a Diophantine condition on the
noncommutativity parameters is found to play a role in the analytical nature of
the non-planar part of the one-loop reduced effective action. Existence of
fixed points for the action may give rise to a new kind of UV/IR mixing.Comment: 30 pages, no figure, version | Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation
Manifolds | heat-kernel approach to uv/ir mixing on isospectral deformation manifolds | perturbative noncommutative manifolds isospectral deformation. curved generalizing moyal planes noncommutative tori rieffel deformation quantization incorporating curved deal deformations essentially way. phenomena kinds isospectral deformations. planar understood diagonal kernel contributions. deformations diophantine noncommutativity planar action. kind pages | non_dup | [] |
2431855 | 10.1007/s00023-005-0235-7 | We prove that "first singularities" in the non-trapped region of the maximal
development of spherically symmetric asymptotically flat data for the
Einstein-Vlasov system must necessarily emanate from the center. The notion of
"first" depends only on the causal structure and can be described in the
language of terminal indecomposable pasts (TIPs). This result suggests a local
approach to proving weak cosmic censorship for this system. It can also be used
to give the first proof of the formation of black holes by the collapse of
collisionless matter from regular initial configurations.Comment: 19 pages, 2 figure | An extension principle for the Einstein-Vlasov system in spherical
symmetry | an extension principle for the einstein-vlasov system in spherical symmetry | singularities trapped maximal spherically asymptotically einstein vlasov necessarily emanate center. notion causal indecomposable pasts tips proving cosmic censorship system. holes collapse collisionless pages | non_dup | [] |
2556723 | 10.1007/s00023-005-0243-7 | Although many physical arguments account for using a modified definition of
time delay in multichannel-type scattering processes, one can hardly find
rigorous results on that issue in the literature. We try to fill in this gap by
showing, both in an abstract setting and in a short-range case, the identity of
the modified time delay and the Eisenbud-Wigner time delay in waveguides. In
the short-range case we also obtain limiting absorption principles, state
spectral properties of the total Hamiltonian, prove the existence of the wave
operators and show an explicit formula for the S-matrix. The proofs rely on
stationary and commutator methods | Time delay and short-range scattering in quantum waveguides | time delay and short-range scattering in quantum waveguides | arguments delay multichannel hardly rigorous literature. fill delay eisenbud wigner delay waveguides. limiting principles matrix. proofs rely stationary commutator | non_dup | [] |
2588047 | 10.1007/s00023-005-0244-6 | Model sets are always Meyer sets, but not vice-versa. This article is about
characterizing model sets (general and regular) amongst the Meyer sets in terms
of two associated dynamical systems. These two dynamical systems describe two
very different topologies on point sets, one local and one global. In model
sets these two are strongly interconnected and this connection is essentially
definitive. The paper is set in the context of multi-colour sets, that is to
say, point sets in which points come in a finite number of colours, that are
loosely coupled together by finite local complexity.Comment: 23pages; to appear in Annales Henri Poincar | A Characterization of Model Multi-colour Sets | a characterization of model multi-colour sets | meyer vice versa. characterizing amongst meyer systems. topologies global. interconnected connection essentially definitive. colour come colours loosely pages annales henri poincar | non_dup | [] |
2556649 | 10.1007/s00023-005-0248-2 | The relativistic Vlasov-Maxwell system of plasma physics is considered with
initial data on a past light cone. This characteristic initial value problem
arises in a natural way as a mathematical framework to study the existence of
solutions isolated from incoming radiation. Various consequences of the
mass-energy conservation and of the absence of incoming radiation condition are
first derived assuming the existence of global smooth solutions. In the
spherically symmetric case, the existence of a unique classical solution in the
future of the initial cone follows by arguments similar to the case of initial
data at time $t=0$. The total mass-energy of spherically symmetric solutions
equals the (properly defined) mass-energy on backward and forward light cones.Comment: 16 pages. Version in pres | On a characteristic initial value problem in Plasma physics | on a characteristic initial value problem in plasma physics | relativistic vlasov maxwell cone. arises mathematical incoming radiation. consequences conservation incoming solutions. spherically cone arguments spherically equals properly backward pages. pres | non_dup | [] |
2527876 | 10.1007/s00023-005-0249-1 | Casimir effect in most general terms may be understood as a backreaction of a
quantum system causing an adiabatic change of the external conditions under
which it is placed. This paper is the second installment of a work scrutinizing
this effect with the use of algebraic methods in quantum theory. The general
scheme worked out in the first part is applied here to the discussion of
particular models. We consider models of the quantum scalar field subject to
external interaction with ``softened'' Dirichlet or Neumann boundary conditions
on two parallel planes. We show that the case of electromagnetic field with
softened perfect conductor conditions on the planes may be reduced to the other
two. The ``softening'' is implemented on the level of the dynamics, and is not
imposed ad hoc, as is usual in most treatments, on the level of observables. We
calculate formulas for the backreaction energy in these models. We find that
the common belief that for electromagnetic field the backreaction force tends
to the strict Casimir formula in the limit of ``removed cutoff'' is not
confirmed by our strict analysis. The formula is model dependent and the
Casimir value is merely a term in the asymptotic expansion of the formula in
inverse powers of the distance of the planes. Typical behaviour of the energy
for large separation of the plates in the class of models considered is a
quadratic fall-of. Depending on the details of the ``softening'' of the
boundary conditions the backreaction force may become repulsive for large
separations.Comment: 50 pages, AMS-LaTeX; to appear in Ann. H. Poincar | Quantum backreaction (Casimir) effect. II. Scalar and electromagnetic
fields | quantum backreaction (casimir) effect. ii. scalar and electromagnetic fields | casimir understood backreaction causing adiabatic placed. installment scrutinizing algebraic theory. worked models. softened dirichlet neumann planes. electromagnetic softened perfect conductor planes two. softening implemented imposed usual treatments observables. formulas backreaction models. belief electromagnetic backreaction tends strict casimir removed cutoff confirmed strict analysis. casimir merely asymptotic powers planes. plates quadratic fall softening backreaction repulsive pages latex ann. poincar | non_dup | [] |
2556969 | 10.1007/s00023-005-0251-7 | We consider an electrically charged particle on the Euclidean plane subjected
to a perpendicular magnetic field which depends only on one of the two
Cartesian co-ordinates. For such a ``unidirectionally constant'' magnetic field
(UMF), which otherwise may be random or not, we prove certain spectral and
transport properties associated with the corresponding one-particle
Schroedinger operator (without scalar potential) by analysing its ``energy-band
structure''. In particular, for an ergodic random UMF we provide conditions
which ensure that the operator's entire spectrum is almost surely absolutely
continuous. This implies that, along the direction in which the random UMF is
constant, the quantum-mechanical motion is almost surely ballistic, while in
the perpendicular direction in the plane one has dynamical localisation. The
conditions are verified, for example, for Gaussian and Poissonian random UMF's
with non-zero mean-values. These results may be viewed as ``random analogues''
of results first obtained by A. Iwatsuka [Publ. RIMS, Kyoto Univ. 21 (1985)
385] and (non-rigorously) by J. E. Mueller [Phys. Rev. Lett. 68 (1992) 385] | Energetic and dynamic properties of a quantum particle in a spatially
random magnetic field with constant correlations along one direction | energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction | electrically euclidean subjected perpendicular cartesian ordinates. unidirectionally schroedinger analysing ergodic ensure surely absolutely continuous. surely ballistic perpendicular localisation. verified poissonian values. viewed analogues iwatsuka publ. rims kyoto univ. rigorously mueller phys. rev. lett. | non_dup | [] |
2380026 | 10.1007/s00023-005-0254-4 | We establish a correspondence between polynomial representations of the
Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect
wave functions. When the deformation parameter is a third root of unity, the
representation degenerates and the wave functions coincide with the domain wall
boundary condition partition function appearing in the conjecture of A.V.
Razumov and Y.G. Stroganov. In particular, this gives a proof of the
identification of the sum of the entries of a O(n) transfer matrix eigenvector
and a six vertex-model partition function, alternative to that of P. Di
Francesco and P. Zinn-Justin.Comment: latex ihp.tex, 2 files, 1 figure, 28 pages
(http://www-spht.cea.fr/articles/T05/087 | Quantum incompressibility and Razumov Stroganov type conjectures | quantum incompressibility and razumov stroganov type conjectures | establish correspondence representations temperley lieb deformations hall functions. deformation unity degenerates coincide partition appearing conjecture a.v. razumov y.g. stroganov. entries eigenvector partition francesco zinn latex ihp.tex files pages | non_dup | [] |
2556997 | 10.1007/s00023-005-0261-5 | We study the perturbation of bound states embedded in the continuous spectrum
which are unstable by the Fermi Golden Rule. The approach to resonance theory
based on spectral deformation is extended to a more general class of quantum
systems characterized by Mourre's inequality and smoothness of the resolvent.
Within the framework of perturbation theory it is still possible to give a
definite meaning to the notion of complex resonance energies and of
corresponding metastable states. The main result is a quasi-exponential decay
estimate up to a controlled error of higher order in perturbation theory.Comment: 17 page | A general resonance theory based on Mourre's inequality | a general resonance theory based on mourre's inequality | perturbation embedded unstable fermi golden rule. deformation mourre inequality smoothness resolvent. perturbation definite meaning notion metastable states. quasi exponential perturbation | non_dup | [] |
2556620 | 10.1007/s00023-006-0263-y | We study the motion of solitary-wave solutions of a family of focusing
generalized nonlinear Schroedinger equations with a confining, slowly varying
external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution
combined with energy estimates allows us to control the motion of the solitary
wave over a long, but finite, time interval. We show that the center of mass of
the solitary wave follows a trajectory close to that of a Newtonian point
particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure | Long time motion of NLS solitary waves in a confining potential | long time motion of nls solitary waves in a confining potential | solitary focusing schroedinger confining slowly lyapunov schmidt decomposition solitary interval. solitary trajectory newtonian pages | non_dup | [] |
2662757 | 10.1007/s00023-006-0269-5 | We derive for Bohmian mechanics topological factors for quantum systems with
a multiply-connected configuration space Q. These include nonabelian factors
corresponding to what we call holonomy-twisted representations of the
fundamental group of Q. We employ wave functions on the universal covering
space of Q. As a byproduct of our analysis, we obtain an explanation, within
the framework of Bohmian mechanics, of the fact that the wave function of a
system of identical particles is either symmetric or anti-symmetric.Comment: 17 pages, no figure | Topological Factors Derived From Bohmian Mechanics | topological factors derived from bohmian mechanics | derive bohmian mechanics topological multiply nonabelian call holonomy twisted representations employ universal covering byproduct explanation bohmian mechanics pages | non_dup | [] |
2557420 | 10.1007/s00023-006-0272-x | We consider a family of non-compact manifolds $X_\eps$ (``graph-like
manifolds'') approaching a metric graph $X_0$ and establish convergence results
of the related natural operators, namely the (Neumann) Laplacian $\laplacian
{X_\eps}$ and the generalised Neumann (Kirchhoff) Laplacian $\laplacian {X_0}$
on the metric graph. In particular, we show the norm convergence of the
resolvents, spectral projections and eigenfunctions. As a consequence, the
essential and the discrete spectrum converge as well. Neither the manifolds nor
the metric graph need to be compact, we only need some natural uniformity
assumptions. We provide examples of manifolds having spectral gaps in the
essential spectrum, discrete eigenvalues in the gaps or even manifolds
approaching a fractal spectrum. The convergence results will be given in a
completely abstract setting dealing with operators acting in different spaces,
applicable also in other geometric situations.Comment: some references added, still 36 pages, 4 figure | Spectral convergence of non-compact quasi-one-dimensional spaces | spectral convergence of non-compact quasi-one-dimensional spaces | manifolds manifolds approaching establish neumann laplacian laplacian generalised neumann kirchhoff laplacian laplacian graph. norm resolvents projections eigenfunctions. converge well. neither manifolds uniformity assumptions. manifolds gaps eigenvalues gaps manifolds approaching fractal spectrum. dealing acting applicable geometric pages | non_dup | [] |
2587514 | 10.1007/s00023-006-0274-8 | We study Hilbert space aspects of the Klein-Gordon equation in
two-dimensional spacetime. We associate to its restriction to a spacelike wedge
a scattering from the past light cone to the future light cone, which is then
shown to be (essentially) the Hankel transform of order zero. We apply this to
give a novel proof, solely based on the causality of this spatio-temporal wave
propagation, of the theorem of de Branges and V. Rovnyak concerning Hankel
pairs with a support property. We recover their isometric expansion as an
application of Riemann's general method for solving Cauchy-Goursat problems of
hyperbolic type.Comment: 24 pages. Final ms, to appear. Improvements on pages 8 and 9, and
15-1 | Spacetime causality in the study of the Hankel transform | spacetime causality in the study of the hankel transform | hilbert klein gordon spacetime. associate restriction spacelike wedge cone cone essentially hankel transform zero. solely causality spatio propagation branges rovnyak concerning hankel property. recover isometric riemann solving cauchy goursat hyperbolic pages. appear. improvements pages | non_dup | [] |
2556656 | 10.1007/s00023-006-0277-5 | We study the semiclassical behaviour of eigenfunctions of quantum systems
with ergodic classical limit. By the quantum ergodicity theorem almost all of
these eigenfunctions become equidistributed in a weak sense. We give a simple
derivation of an upper bound of order $\abs{\ln\hbar}^{-1}$ on the rate of
quantum ergodicity if the classical system is ergodic with a certain rate. In
addition we obtain a similar bound on transition amplitudes if the classical
system is weak mixing. Both results generalise previous ones by Zelditch. We
then extend the results to some classes of quantised maps on the torus and
obtain a logarithmic rate for perturbed cat-maps and a sharp algebraic rate for
parabolic maps.Comment: 18 page | Upper bounds on the rate of quantum ergodicity | upper bounds on the rate of quantum ergodicity | semiclassical eigenfunctions ergodic limit. ergodicity eigenfunctions equidistributed sense. derivation hbar ergodicity ergodic rate. amplitudes mixing. generalise zelditch. extend quantised torus logarithmic perturbed sharp algebraic parabolic | non_dup | [] |
2557376 | 10.1007/s00023-006-0280-x | We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and
open diagonal soliton-preserving boundary conditions. By employing analytical
Bethe ansatz techniques we are able to determine the spectrum and the
corresponding Bethe ansatz equations for the general case, where each site of
the spin chain is associated to any representation of U_{q}(gl(N)).
In the case of open spin chain, we study finite dimensional representations
of the quantum reflection algebra, and prove in full generality that the
pseudo-vacuum is a highest weight of the monodromy matrix.
For these two types of spin chain, we study the (generalized) "algebraic"
fusion procedures, which amount to construct the quantum contraction and the
Sklyanin determinant for the affine U_{q}(gl(N)) and quantum reflection
algebras. We also determine the symmetry algebra of these two types of spin
chains, including general K and K^+ diagonal matrices for the open case.
The case of open spin chains with soliton non-preserving boundary conditions
is also presented in the framework of quantum twisted Yangians. The symmetry
algebra of this spin chains is studied. We also give an exhaustive
classification of the invertible matricial solutions to the corresponding
reflection equation.Comment: 48 pages; Bounds on parameters Mj corrected; References added;
Examples adde | Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and
open spin chains in any representation | spectrum and bethe ansatz equations for the u_ {q}(gl(n)) closed and open spin chains in any representation | integrable diagonal soliton preserving conditions. employing bethe ansatz bethe ansatz representations reflection generality pseudo monodromy matrix. algebraic fusion contraction sklyanin determinant affine reflection algebras. chains diagonal case. chains soliton preserving twisted yangians. chains studied. exhaustive invertible matricial reflection pages bounds corrected adde | non_dup | [] |
2588785 | 10.1007/s00023-006-0281-9 | We study the Yangians Y(a) associated with the simple Lie algebras a of type
B, C or D. The algebra Y(a) can be regarded as a quotient of the extended
Yangian X(a) whose defining relations are written in an R-matrix form. In this
paper we are concerned with the algebraic structure and representations of the
algebra X(a). We prove an analog of the Poincare-Birkhoff-Witt theorem for X(a)
and show that the Yangian Y(a) can be realized as a subalgebra of X(a).
Furthermore, we give an independent proof of the classification theorem for the
finite-dimensional irreducible representations of X(a) which implies the
corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit
constructions for all fundamental representation of the Yangians.Comment: 65 page | On the R-matrix realization of Yangians and their representations | on the r-matrix realization of yangians and their representations | yangians algebras regarded quotient yangian defining form. concerned algebraic representations analog poincare birkhoff witt yangian realized subalgebra irreducible representations drinfeld yangians constructions | non_dup | [] |
2590425 | 10.1007/s00023-006-0283-7 | The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation,
which is not a deformation of the trivial, is considered. Its FRT dual algebra
$s03_F$ is studied. The Baxterisation of the dual algebra is given in two
different parametrisations. The finite-dimensional representations of $s03_F$
are considered. Diagonalisations of the braid matrices are used to yield
remarkable insights concerning representations of the L-algebra and to
formulate the fusion of finite-dimensional representations. Possible
applications are considered, in particular, an exotic eight-vertex model and an
integrable spin-chain model.Comment: 24 pages, Latex; V2: revised subsection 4.1, added 9 references, to
appear in Annales Henri Poincare in the volume dedicated to D. Arnaudo | Exotic Bialgebra S03: Representations, Baxterisation and Applications | exotic bialgebra s03: representations, baxterisation and applications | exotic bialgebra baxter deformation trivial considered. studied. baxterisation parametrisations. representations considered. diagonalisations braid remarkable insights concerning representations formulate fusion representations. exotic eight integrable pages latex revised subsection annales henri poincare dedicated arnaudo | non_dup | [] |
2529065 | 10.1007/s00023-006-0284-6 | The method of bosonization is extended to the case when a dissipationless
point-like defect is present in space-time. Introducing the chiral components
of a massless scalar field, interacting with the defect in two dimensions, we
construct the associated vertex operators. The main features of the
corresponding vertex algebra are established. As an application of this
framework we solve the massless Thirring model with defect. We also construct
the vertex representation of the sl(2) Kac-Moody algebra, describing the
complex interplay between the left and right sectors due to the interaction
with the defect. The Sugawara form of the energy-momentum tensor is also
explored.Comment: 23 pages, 1 figur | Bosonization and Vertex Algebras with Defects | bosonization and vertex algebras with defects | bosonization dissipationless defect time. introducing chiral massless interacting defect operators. established. solve massless thirring defect. moody describing interplay sectors defect. sugawara pages figur | non_dup | [] |
2529881 | 10.1007/s00023-006-0287-3 | Bound state excitations of the spin 1/2-XYZ model are considered inside the
Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral
Equations. Of course, these bound states go to the sine-Gordon breathers in the
suitable limit and therefore the scattering factors between them are explicitly
computed by inspecting the corresponding Non-Linear Integral Equations. As a
consequence, abstracting from the physical model the Zamolodchikov-Faddeev
algebra of two $n$-th elliptic breathers defines a tower of $n$-order Deformed
Virasoro Algebras, reproducing the $n=1$ case the usual well-known algebra of
Shiraishi-Kubo-Awata-Odake \cite{SKAO}.Comment: Latex version, 13 page | The elliptic scattering theory of the 1/2-XYZ and higher order Deformed
Virasoro Algebras | the elliptic scattering theory of the 1/2-xyz and higher order deformed virasoro algebras | excitations bethe ansatz exploiting equations. sine gordon breathers explicitly inspecting equations. abstracting zamolodchikov faddeev elliptic breathers defines tower deformed virasoro algebras reproducing usual shiraishi kubo awata odake cite skao .comment latex | non_dup | [] |
2386924 | 10.1007/s00023-006-0290-8 | We discuss irreducible highest weight representations of the sl(2) loop
algebra and reducible indecomposable ones in association with the sl(2) loop
algebra symmetry of the six-vertex model at roots of unity. We formulate an
elementary proof that every highest weight representation with distinct
evaluation parameters is irreducible. We present a general criteria for a
highest weight representation to be irreducble. We also give an example of a
reducible indecomposable highest weight representation and discuss its
dimensionality.Comment: 10 pages, no figures, submitted to the proceedings of the
international workshop ``Recent Advances in Quantum Integrable Systems'',
September 6-9, 2005, LAPTH, Annecy-le-Vieux, Franc | The six-vertex model at roots of unity and some highest weight
representations of the sl(2) loop algebra | the six-vertex model at roots of unity and some highest weight representations of the sl(2) loop algebra | irreducible representations reducible indecomposable roots unity. formulate elementary irreducible. irreducble. reducible indecomposable pages submitted workshop advances integrable september lapth annecy vieux franc | non_dup | [] |
2583678 | 10.1007/s00023-006-0292-6 | The matrix elements of the $2\times 2$ fusion of Baxter's elliptic
$R$-matrix, $R^{(2,2)}(u)$, are given explicitly. Based on a note by Jimbo, we
give a formula which show that $R^{(2,2)}(u)$ is gauge equivalent to Fateev's
$R$-matrix for the 21-vertex model. Then the crossing symmetry formula for
$R^{(2,2)}(u)$ is derived. We also consider the fusion of the vertex-face
correspondence relation and derive a crossing symmetry relation between the
fusion of the intertwining vectors and their dual vectors.Comment: To appear in the proceedings of the workshop ``Solvable Lattice
Models 2004", July 20--23, 2004, RIMS Koukyuroku, Kyoto Universit | Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face
Correspondence | fusion of baxter's elliptic $r$-matrix and the vertex-face correspondence | fusion baxter elliptic explicitly. jimbo fateev model. crossing derived. fusion correspondence derive crossing fusion intertwining workshop solvable rims koukyuroku kyoto universit | non_dup | [] |
2393251 | 10.1007/s00023-006-0294-4 | The spin-1/2 zig-zag Heisenberg ladder (J_1 - J_2 model) is considered. A new
representation for the model is found and a saddle point approximation over the
spin-liquid order parameter < \vec \sigma_{n-1}(\vec \sigma_{n}\times \vec
\sigma_{n+1}) > is performed. Corresponding effective action is derived and
analytically analyzed. We observe the presence of phase transitions at values
J_2/J_1=0.231 and J_2/J_1=1/2.Comment: 12 pages, 6 figures. Contribution to the Annales Henri Poincare
volume dedicated to the memory of Daniel Arnaudo | Mean-field theory for Heisenberg zigzag ladder: Ground state energy and
spontaneous symmetry breaking | mean-field theory for heisenberg zigzag ladder: ground state energy and spontaneous symmetry breaking | heisenberg ladder considered. saddle sigma sigma sigma performed. analytically analyzed. pages figures. annales henri poincare dedicated daniel arnaudo | non_dup | [] |
2388837 | 10.1007/s00023-006-0295-3 | The two-site Bose--Hubbard model is a simple model used to study Josephson
tunneling between two Bose--Einstein condensates. In this work we give an
overview of some mathematical aspects of this model. Using a classical
analysis, we study the equations of motion and the level curves of the
Hamiltonian. Then, the quantum dynamics of the model is investigated using
direct diagonalisation of the Hamiltonian. In both of these analyses, the
existence of a threshold coupling between a delocalised and a self-trapped
phase is evident, in qualitative agreement with experiments. We end with a
discussion of the exact solvability of the model via the algebraic Bethe
ansatz.Comment: 10 pages, 5 figures, submitted for publication in Annales Henri
Poincar | The two-site Bose--Hubbard model | the two-site bose--hubbard model | bose hubbard josephson tunneling bose einstein condensates. overview mathematical model. hamiltonian. diagonalisation hamiltonian. delocalised trapped evident qualitative experiments. solvability algebraic bethe pages submitted publication annales henri poincar | non_dup | [] |
2557767 | 10.1007/s00023-006-0297-1 | We study the higher-order correlation functions of covariant families of
observables associated with random Schr\"odinger operators on the lattice in
the strong disorder regime. We prove that if the distribution of the random
variables has a density analytic in a strip about the real axis, then these
correlation functions are analytic functions of the energy outside of the
planes corresponding to coincident energies. In particular, this implies the
analyticity of the density of states, and of the current-current correlation
function outside of the diagonal. Consequently, this proves that the
current-current correlation function has an analytic density outside of the
diagonal at strong disorder | Smoothness of Correlations in the Anderson Model at Strong Disorder | smoothness of correlations in the anderson model at strong disorder | covariant families observables schr odinger disorder regime. analytic strip analytic planes coincident energies. analyticity diagonal. proves analytic diagonal disorder | non_dup | [] |
2590139 | 10.1007/s00023-006-0300-x | We study extreme values of desymmetrized eigenfunctions (so called Hecke
eigenfunctions) for the quantized cat map, a quantization of a hyperbolic
linear map of the torus.
In a previous paper it was shown that for prime values of the inverse Planck
constant N=1/h, such that the map is diagonalizable (but not upper triangular)
modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this
paper is to show that the same holds for any prime N provided that the map is
not upper triangular modulo N.
We also find that the supremum norms of Hecke eigenfunctions are << N^epsilon
for all epsilon>0 in the case of N square free.Comment: 16 pages. Introduction expanded; comparison with supremum norms of
eigenfunctions of the Laplacian added. Bound for square free N adde | Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps | bounds on supremum norms for hecke eigenfunctions of quantized cat maps | extreme desymmetrized eigenfunctions hecke eigenfunctions quantized quantization hyperbolic torus. prime planck diagonalizable triangular modulo hecke eigenfunctions uniformly bounded. prime triangular modulo supremum norms hecke eigenfunctions epsilon epsilon pages. expanded supremum norms eigenfunctions laplacian added. adde | non_dup | [] |
2557805 | 10.1007/s00023-006-0302-8 | We analyze Schr\"odinger operators whose potential is given by a singular
interaction supported on a sub-manifold of the ambient space. Under the
assumption that the operator has at least two eigenvalues below its essential
spectrum we derive estimates on the lowest spectral gap. In the case where the
sub-manifold is a finite curve in two dimensional Euclidean space the size of
the gap depends only on the following parameters: the length, diameter and
maximal curvature of the curve, a certain parameter measuring the injectivity
of the curve embedding, and a compact sub-interval of the open, negative energy
half-axis which contains the two lowest eigenvalues.Comment: 24 pages. To appear in slightly different form in Annales Henri
Poincar | Lower bounds on the lowest spectral gap of singular potential
Hamiltonians | lower bounds on the lowest spectral gap of singular potential hamiltonians | analyze schr odinger singular manifold ambient space. eigenvalues derive gap. manifold euclidean maximal curvature measuring injectivity embedding pages. annales henri poincar | non_dup | [] |
52455389 | 10.1007/s00023-006-0308-2 | International audienceThe Fourier transform of orthogonal polynomials with respect to their own orthogonality measure defines the family of Fourier-Bessel functions. We study the asymptotic behaviour of these functions and of their products, for large real values of the argument. By employing a Mellin analysis we construct a general framework to exhibit the relation of the asymptotic decay laws to certain dimensions of the orthogonality measure, that are defined via the divergence abscissas of suitable integrals. The unifying rôle of Mellin transform techniques in deriving classical and new results is underlined | The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin Transform Techniques | the asymptotic behaviour of the fourier transforms of orthogonal polynomials i: mellin transform techniques | audiencethe fourier transform orthogonal polynomials orthogonality defines fourier bessel functions. asymptotic argument. employing mellin exhibit asymptotic laws orthogonality divergence abscissas integrals. unifying rôle mellin transform deriving underlined | non_dup | [] |
2590493 | 10.1007/s00023-006-0311-7 | We relate two types of phase space distributions associated to eigenfunctions
$\phi_{ir_j}$ of the Laplacian on a compact hyperbolic surface $X_{\Gamma}$:
(1) Wigner distributions $\int_{S^*\X} a dW_{ir_j}=< Op(a)\phi_{ir_j},
\phi_{ir_j}>_{L^2(\X)}$, which arise in quantum chaos. They are invariant under
the wave group.
(2) Patterson-Sullivan distributions $PS_{ir_j}$, which are the residues of
the dynamical zeta-functions $\lcal(s; a): = \sum_\gamma
\frac{e^{-sL_\gamma}}{1-e^{-L_\gamma}} \int_{\gamma_0} a$ (where the sum runs
over closed geodesics) at the poles $s = {1/2} + ir_j$. They are invariant
under the geodesic flow.
We prove that these distributions (when suitably normalized) are
asymptotically equal as $r_j \to \infty$. We also give exact relations between
them. This correspondence gives a new relation between classical and quantum
dynamics on a hyperbolic surface, and consequently a formulation of quantum
ergodicity in terms of classical ergodic theory.Comment: 54 pages, no figures. Added some reference | Patterson-Sullivan distributions and quantum ergodicity | patterson-sullivan distributions and quantum ergodicity | relate eigenfunctions laplacian hyperbolic gamma wigner arise chaos. group. patterson sullivan zeta lcal gamma frac gamma gamma gamma runs geodesics poles geodesic flow. suitably asymptotically infty them. correspondence hyperbolic formulation ergodicity ergodic pages figures. | non_dup | [] |
2591533 | 10.1007/s00023-006-0313-5 | This work results from our attempts to solve Boltzmann-Sinai's hypothesis
about the ergodicity of hard ball gases. A crucial element in the studies of
the dynamics of hard balls is the analysis of special hypersurfaces in the
phase space consisting of degenerate trajectories (which lack complete
hyperbolicity). We prove that if a flow-invariant hypersurface $J$ in the phase
space of a semi-dispersing billiard has a negative Lyapunov function, then the
volume of the forward image of $J$ grows at least linearly in time. Our proof
is independent of the solution of the Boltzmann-Sinai hypothesis, and we
provide a complete and self-contained argument here | Flow-invariant hypersurfaces in semi-dispersing billiards | flow-invariant hypersurfaces in semi-dispersing billiards | attempts solve boltzmann sinai ergodicity ball gases. crucial balls hypersurfaces consisting degenerate trajectories hyperbolicity hypersurface dispersing billiard lyapunov grows linearly time. boltzmann sinai argument | non_dup | [] |
2600404 | 10.1007/s00023-006-0315-3 | To study the location of poles for the acoustic scattering matrix for two
strictly convex obstacles with smooth boundaries, one uses an approximation of
the quantized billiard operator $M$ along the trapped ray between the two
obstacles. Using this method Ikawa and G{\'e}rard established the existence of
parallel rows of poles in a strip $Im z\leq c$ as $Re z$ tends to infinity.
Assuming that the boundaries are analytic and the eigenvalues of Poincar{\'e}
map are non-resonant we use the Birkhoff normal form for $M$ to improve this
result and to get the complete asymptotic expansions for the poles in any
logarithmic neighborhood of real axis | Scattering Poles Near the Real Axis for Two Strictly Convex Obstacles | scattering poles near the real axis for two strictly convex obstacles | poles acoustic strictly convex obstacles boundaries quantized billiard trapped obstacles. ikawa rard rows poles strip tends infinity. boundaries analytic eigenvalues poincar resonant birkhoff asymptotic expansions poles logarithmic neighborhood | non_dup | [] |
2557480 | 10.1007/s00023-006-0316-2 | The quasi-static evolution of steady states far from equilibrium is
investigated from the point of view of quantum statistical mechanics. As a
concrete example of a thermodynamic system, a two-level quantum dot coupled to
several reservoirs of free fermions at different temperatures is considered. A
novel adiabatic theorem for unbounded and nonnormal generators of evolution is
proven and applied to study the quasi-static evolution of nonequilibrium steady
states (NESS) of the coupled system.Comment: 39 pages. Some typos corrected. To appear in Ann. Henri Poincar | On the quasi-static evolution of nonequilibrium steady states | on the quasi-static evolution of nonequilibrium steady states | quasi steady mechanics. concrete thermodynamic reservoirs fermions considered. adiabatic unbounded nonnormal generators proven quasi nonequilibrium steady ness pages. typos corrected. ann. henri poincar | non_dup | [] |
2557587 | 10.1007/s00023-006-0320-1 | We investigate regularity properties of molecular one-electron densities rho
near the nuclei. In particular we derive a representation rho(x)=mu(x)*(e^F(x))
with an explicit function F, only depending on the nuclear charges and the
positions of the nuclei, such that mu belongs to C^{1,1}(R^3), i.e., mu has
locally essentially bounded second derivatives. An example constructed using
Hydrogenic eigenfunctions shows that this regularity result is sharp. For
atomic eigenfunctions which are either even or odd with respect to inversion in
the origin, we prove that mu is even C^{2,\alpha}(R^3) for all alpha in (0,1).
Placing one nucleus at the origin we study rho in polar coordinates x=r*omega
and investigate rho'(r,omega) and rho''(r,omega) for fixed omega as r tends to
zero. We prove non-isotropic cusp conditions of first and second order, which
generalize Kato's classical result.Comment: 19 page | Non-isotropic cusp conditions and regularity of the electron density of
molecules at the nuclei | non-isotropic cusp conditions and regularity of the electron density of molecules at the nuclei | regularity densities nuclei. derive charges nuclei belongs i.e. locally essentially derivatives. hydrogenic eigenfunctions regularity sharp. eigenfunctions inversion alpha alpha placing nucleus polar omega omega omega omega tends zero. isotropic cusp generalize kato | non_dup | [] |
2556279 | 10.1007/s00023-006-0322-z | For Schroedinger operators (including those with magnetic fields) with
singular (locally integrable) scalar potentials on manifolds of bounded
geometry, we study continuity properties of some related integral kernels: the
heat kernel, the Green function, and also kernels of some other functions of
the operator. In particular, we show the joint continuity of the heat kernel
and the continuity of the Green function outside the diagonal. The proof makes
intensive use of the Lippmann-Schwinger equation.Comment: 38 pages, major revision; to appear in Annales Henri Poincare (2007 | Continuity properties of integral kernels associated with Schroedinger
operators on manifolds | continuity properties of integral kernels associated with schroedinger operators on manifolds | schroedinger singular locally integrable potentials manifolds continuity kernels kernel kernels operator. continuity kernel continuity diagonal. intensive lippmann schwinger pages revision annales henri poincare | non_dup | [] |
2434543 | 10.1007/s00023-006-0323-3 | We study formal expansions of asymptotically flat solutions to the static
vacuum field equations which are determined by minimal sets of freely
specifyable data referred to as `null data'. These are given by sequences of
symmetric trace free tensors at space-like infinity of increasing order. They
are 1:1 related to the sequences of Geroch multipoles. Necessary and sufficient
growth estimates on the null data are obtained for the formal expansions to be
absolutely convergent. This provides a complete characterization of all
asymptotically flat solutions to the static vacuum field equations.Comment: 65 page | Static vacuum solutions from convergent null data expansions at
space-like infinity | static vacuum solutions from convergent null data expansions at space-like infinity | formal expansions asymptotically freely specifyable referred trace tensors infinity order. geroch multipoles. formal expansions absolutely convergent. asymptotically | non_dup | [] |
2594067 | 10.1007/s00023-006-0325-1 | We study the theory of scattering for the Maxwell-Schr"odinger system in
space dimension 3, in the Coulomb gauge. We prove the existence of modified
wave operators for that system with no size restriction on the Schr"odinger and
Maxwell asymptotic data and we determine the asymptotic behaviour in time of
solutions in the range of the wave operators. The method consists in partially
solving the Maxwell equations for the potentials, substituting the result into
the Schr"odinger equation, which then becomes both nonlinear and nonlocal in
time. The Schr"odinger function is then parametrized in terms of an amplitude
and a phase satisfying a suitable auxiliary system, and the Cauchy problem for
that system, with prescribed asymptotic behaviour determined by the asymptotic
data, is solved by an energy method, thereby leading to solutions of the
original system with prescribed asymptotic behaviour in time. This paper is the
generalization of a previous paper with the same title. However it is entirely
selfcontained and can be read without any previous knowledge of the latter.Comment: latex 96 page | Long Range Scattering and Modified Wave Operators for the
Maxwell-Schr"odinger System II. The general case | long range scattering and modified wave operators for the maxwell-schr"odinger system ii. the general case | maxwell schr odinger coulomb gauge. restriction schr odinger maxwell asymptotic asymptotic operators. partially solving maxwell potentials substituting schr odinger nonlocal time. schr odinger parametrized satisfying auxiliary cauchy prescribed asymptotic asymptotic solved thereby prescribed asymptotic time. generalization title. entirely selfcontained read latex | non_dup | [] |
2557468 | 10.1007/s00023-007-0326-8 | In the framework of the theory of an electron in a periodic potential, we
reconsider the longstanding problem of the existence of smooth and periodic
quasi-Bloch functions, which is shown to be equivalent to the triviality of the
Bloch bundle. By exploiting the time-reversal symmetry of the Hamiltonian and
some bundle-theoretic methods, we show that the problem has a positive answer
for any d < 4, thus generalizing a previous result by G. Nenciu. We provide a
general formulation of the result, aiming at the application to the Dirac
equation with a periodic potential and to piezoelectricity.Comment: 20 pages, no figure | Triviality of Bloch and Bloch-Dirac bundles | triviality of bloch and bloch-dirac bundles | reconsider longstanding quasi bloch triviality bloch bundle. exploiting reversal bundle theoretic answer generalizing nenciu. formulation aiming dirac pages | non_dup | [] |
2434686 | 10.1007/s00023-007-0333-9 | Some future global properties of cosmological solutions for the
Einstein-Vlasov-Maxwell system with surface symmetry are presented. Global
existence is proved, the homogeneous spacetimes are future complete for causal
trajectories, and the same is true for inhomogeneous plane-symmetric solutions
with small initial data. In the latter case some decay properties are also
obtained at late times. Similar but slightly weaker results hold for hyperbolic
symmetry.Comment: 34 pages, version to be published in AH | On surface-symmetric spacetimes with collisionless and charged matter | on surface-symmetric spacetimes with collisionless and charged matter | cosmological einstein vlasov maxwell presented. proved homogeneous spacetimes causal trajectories inhomogeneous data. times. weaker hold hyperbolic pages | non_dup | [] |
2558319 | 10.1007/s00023-007-0337-5 | The bipolaron are two electrons coupled to the elastic deformations of an
ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the
Coulomb repulsion dominates, the lowest energy states are two well separated
polarons. Otherwise the electrons form a bound pair. We prove the validity of
the Pekar-Tomasevich energy functional in the strong coupling limit, yielding
estimates on the coupling parameters for which the binding energy is strictly
positive. Under the condition of a strictly positive binding energy we prove
the existence of a ground state at fixed total momentum $P$, provided $P$ is
not too large.Comment: 31 page | The bipolaron in the strong coupling limit | the bipolaron in the strong coupling limit | bipolaron elastic deformations ionic crystal. hlich approximation. coulomb repulsion dominates separated polarons. pair. validity pekar tomasevich yielding strictly positive. strictly | non_dup | [] |
2557955 | 10.1007/s00023-007-0338-4 | We consider the Laplacian in $\mathbb{R}^n$ perturbed by a finite number of
distant perturbations those are abstract localized operators. We study the
asymptotic behaviour of the discrete spectrum as the distances between
perturbations tend to infinity. The main results are the convergence theorem
and the asymptotics expansions for the eigenelements. Some examples of the
possible distant perturbations are given; they are potential, second order
differential operator, magnetic Schrodinger operator, integral operator, and
$\d$-potential | Distant perturbations of the Laplacian in a multi-dimensional space | distant perturbations of the laplacian in a multi-dimensional space | laplacian mathbb perturbed distant perturbations localized operators. asymptotic distances perturbations tend infinity. asymptotics expansions eigenelements. distant perturbations schrodinger | non_dup | [] |
2557935 | 10.1007/s00023-007-0341-9 | We consider a natural generalization of Haag duality to the case in which the
observable algebra is restricted to a subset of the space-time and is not
irreducible: the commutant and the causal complement have to be considered
relatively to the ambient space. We prove this relative form of Haag duality
under quite general conditions for the free scalar and electromagnetic field of
space dimension d>1 in the vacuum representation. Such property is interesting
in view of a theory of superselection sectors for the electromagnetic field.Comment: 22 page | Relative Haag Duality for the Free Field in Fock Representation | relative haag duality for the free field in fock representation | generalization haag duality observable restricted irreducible commutant causal complement ambient space. haag duality electromagnetic representation. superselection sectors electromagnetic | non_dup | [] |
2557574 | 10.1007/s00023-007-0346-4 | We study a small quantum system (e.g. a simplified model for an atom or
molecule) interacting with two bosonic or fermionic reservoirs (say, photon or
phonon fields). We show that the combined system has a family of stationary
states, parametrized by two numbers $T_1$, $T_2$ (``reservoir temperatures'').
If $T_1\neq T_2$, then these states are non-equilibrium, stationary states
(NESS). In the latter case we show that they have nonvanishing heat fluxes and
positive entropy production. Furthermore, we show that these states are
dynamically asymptotically stable. The latter means that the evolution with an
initial condition, normal with respect to any state where the reservoirs are in
equilibria at temperatures $T_1$ and $T_2$, converges to the corresponding
NESS. Our results are valid for the temperatures satisfying the bound
$\min(T_1, T_2) > g^{2+\alpha}$, where $g$ is the coupling constant and $0<
\alpha<1$ is a power related to the infra-red behaviour of the coupling
functions.Comment: 1 figure. To appear in Ann. H. Poincar | Theory of Non-Equilibrium Sationary States as a Theory of Resonances | theory of non-equilibrium sationary states as a theory of resonances | e.g. simplified atom molecule interacting bosonic fermionic reservoirs phonon stationary parametrized reservoir stationary ness nonvanishing fluxes production. dynamically asymptotically stable. reservoirs equilibria converges ness. valid satisfying alpha alpha infra figure. ann. poincar | non_dup | [] |
2601538 | 10.1007/s00023-007-0348-2 | The Witten spinorial argument has been adapted in several works over the
years to prove positivity of mass in the asymptotically AdS and asymptotically
hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar
curvature rigidity result and a positive mass theorem for asymptotically
hyperbolic manifolds that do not require a spin assumption. The positive mass
theorem is reduced to the rigidity case by a deformation construction near the
conformal boundary. The proof of the rigidity result is based on a study of
minimizers of the BPS brane action.Comment: 42 pages, 2 figure | Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds | rigidity and positivity of mass for asymptotically hyperbolic manifolds | witten spinorial argument adapted positivity asymptotically asymptotically hyperbolic settings dimensions. curvature rigidity asymptotically hyperbolic manifolds assumption. rigidity deformation conformal boundary. rigidity minimizers brane pages | non_dup | [] |
1937598 | 10.1007/s00023-007-0349-1 | It is known that, in an asymptotically flat spacetime, null infinity cannot
act as an initial-value surface for massive real scalar fields. Exploiting
tools proper of harmonic analysis on hyperboloids and global norm estimates for
the wave operator, we show that it is possible to circumvent such obstruction
at least in Minkowski spacetime. Hence we project norm-finite solutions of the
Klein-Gordon equation of motion in data on null infinity and, eventually, we
interpret them in terms of boundary free field theory.Comment: 26 page | Projecting Massive Scalar Fields to Null Infinity | projecting massive scalar fields to null infinity | asymptotically spacetime infinity massive fields. exploiting proper harmonic hyperboloids norm circumvent obstruction minkowski spacetime. norm klein gordon infinity eventually interpret | non_dup | [] |
2558532 | 10.1007/s00023-007-0352-6 | We study the volume of nodal sets for eigenfunctions of the Laplacian on the
standard torus in two or more dimensions. We consider a sequence of eigenvalues
$4\pi^2\eigenvalue$ with growing multiplicity $\Ndim\to\infty$, and compute the
expectation and variance of the volume of the nodal set with respect to a
Gaussian probability measure on the eigenspaces. We show that the expected
volume of the nodal set is $const \sqrt{\eigenvalue}$. Our main result is that
the variance of the volume normalized by $\sqrt{\eigenvalue}$ is bounded by
$O(1/\sqrt{\Ndim})$, so that the normalized volume has vanishing fluctuations
as we increase the dimension of the eigenspace.Comment: 20 pages, Was accepted for publication in the Annales Henri Poincar | On the volume of nodal sets for eigenfunctions of the Laplacian on the
torus | on the volume of nodal sets for eigenfunctions of the laplacian on the torus | nodal eigenfunctions laplacian torus dimensions. eigenvalues eigenvalue growing multiplicity ndim infty expectation nodal eigenspaces. nodal const sqrt eigenvalue sqrt eigenvalue sqrt ndim vanishing pages publication annales henri poincar | non_dup | [] |
2600222 | 10.1007/s00023-007-0353-5 | We consider an open manifold which is the interior of a compact manifold with
boundary. Assuming gauge invariance, we classify magnetic fields with compact
support into being trapping or non-trapping. We study spectral properties of
the associated magnetic Laplacian for a class of Riemannian metrics which
includes complete hyperbolic metrics of finite volume. When $B$ is
non-trapping, the magnetic Laplacian has nonempty essential spectrum. Using
Mourre theory, we show the absence of singular continuous spectrum and the
local finiteness of the point spectrum. When $B$ is trapping, the spectrum is
discrete and obeys the Weyl law. The existence of trapping magnetic fields with
compact support depends on cohomological conditions, indicating a new and very
strong long-range effect.
In the non-gauge invariant case, we exhibit a strong Aharonov-Bohm effect. On
hyperbolic surfaces with at least two cusps, we show that the magnetic
Laplacian associated to every magnetic field with compact support has purely
discrete spectrum for some choices of the vector potential, while other choices
lead to a situation of limit absorption principle.
We also study perturbations of the metric. We show that in the Mourre theory
it is not necessary to require a decay of the derivatives of the perturbation.
This very singular perturbation is then brought closer to the perturbation of a
potential.Comment: 52 pages. Revised version: references added. To appear in Annales
Henri Poincar\' | Spectral analysis of magnetic Laplacians on conformally cusp manifolds | spectral analysis of magnetic laplacians on conformally cusp manifolds | manifold interior manifold boundary. invariance classify trapping trapping. laplacian riemannian metrics hyperbolic metrics volume. trapping laplacian nonempty spectrum. mourre singular finiteness spectrum. trapping obeys weyl law. trapping cohomological effect. exhibit aharonov bohm effect. hyperbolic cusps laplacian purely choices choices principle. perturbations metric. mourre derivatives perturbation. singular perturbation brought closer perturbation pages. revised added. annales henri poincar | non_dup | [] |
1940185 | 10.1007/s00023-007-0354-4 | We consider a class of translationally invariant magnetic fields such that
the corresponding potential has a constant direction.
Our goal is to study basic spectral properties of the Schr\"odinger operator
${\bf H}$ with such a potential. In particular, we show that the spectrum of
${\bf H}$ is absolutely continuous and we find its location. Then we study the
long-time behaviour of solutions $\exp(-i {\bf H} t)f$ of the time dependent
Schr\"odinger equation. It turnes out that a quantum particle remains localized
in the plane orthogonal to the direction of the potential. Its propagation in
this direction is determined by group velocities. It is to a some extent
similar to a evolution of a one-dimensional free particle but "exits" to
$+\infty$ and $-\infty$ might be essentially different | On spectral properties of translationally invariant magnetic
Schr\"odinger operators | on spectral properties of translationally invariant magnetic schr\"odinger operators | translationally direction. goal schr odinger potential. absolutely location. schr odinger equation. turnes localized orthogonal potential. propagation velocities. exits infty infty essentially | non_dup | [] |
1960759 | 10.1007/s00023-008-0359-7 | An algebra previously proposed as an asymptotic field structure in
electrodynamics is considered in respect of localization properties of fields.
Fields are 'spatially local' -- localized in regions resulting as unions of two
intersecting (solid) lightcones: a future- and a past-lightcone. This
localization remains in concord with the usual idealizations connected with the
scattering theory. Fields thus localized naturally include infrared
characteristics normally placed at spacelike infinity and form a structure
respecting Gauss law. When applied to the description of the radiation of an
external classical current the model is free of 'infrared catastrophe'.Comment: 30 pages; accepted for publication in Ann. Henri Poincare; a few
minor correction | Infrared problem and spatially local observables in electrodynamics | infrared problem and spatially local observables in electrodynamics | asymptotic electrodynamics localization fields. spatially localized unions intersecting lightcones lightcone. localization concord usual idealizations theory. localized naturally infrared normally placed spacelike infinity respecting gauss law. infrared catastrophe .comment pages publication ann. henri poincare minor | non_dup | [] |
1947697 | 10.1007/s00023-008-0365-9 | We consider a system of N nonrelativistic particles of spin 1/2 interacting
with the quantized Maxwell field (mass zero and spin one) in the limit when the
particles have a small velocity, imposing to the interaction an ultraviolet
cutoff, but no infrared cutoff.
Two ways to implement the limit are considered: c going to infinity with the
velocity v of the particles fixed, the case for which rigorous results have
already been discussed in the literature, and v going to 0 with c fixed. The
second case can be rephrased as the limit of heavy particles, m_{j} -->
epsilon^{-2}m_{j}, observed over a long time, t --> epsilon^{-1}t, epsilon -->
0^{+}, with kinetic energy E_{kin} = Or(1).
Focusing on the second approach we construct subspaces which are invariant
for the dynamics up to terms of order epsilon sqrt{log(epsilon^{-1})} and
describe effective dynamics, for the particles only, inside them. At the lowest
order the particles interact through Coulomb potentials. At the second one,
epsilon^{2}, the mass gets a correction of electromagnetic origin and a
velocity dependent interaction, the Darwin term, appears.
Moreover, we calculate the radiated piece of the wave function, i. e., the
piece which leaks out of the almost invariant subspaces and calculate the
corresponding radiated energy.Comment: 46 pages, no figures. Minor changes in the introduction and
correction of some typos. Version accepted for publication in Annales Henri
Poincare | Quasi-static Limits in Nonrelativistic Quantum Electrodynamics | quasi-static limits in nonrelativistic quantum electrodynamics | nonrelativistic interacting quantized maxwell imposing ultraviolet cutoff infrared cutoff. ways implement going infinity rigorous going fixed. rephrased epsilon epsilon epsilon focusing subspaces epsilon sqrt epsilon them. interact coulomb potentials. epsilon gets electromagnetic darwin appears. radiated piece piece leaks subspaces radiated pages figures. minor typos. publication annales henri poincare | non_dup | [] |
1963624 | 10.1007/s00023-008-0368-6 | We construct large families of initial data sets for the vacuum Einstein
equations with positive cosmological constant which contain exactly Delaunay
ends; these are non-trivial initial data sets which coincide with those for the
Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the
purely Riemannian geometric point of view, this produces complete, constant
positive scalar curvature metrics with exact Delaunay ends which are not
globally Delaunay. The ends can be used to construct new compact initial data
sets via gluing constructions. The construction provided applies to more
general situations where the asymptotic geometry may have non-spherical
cross-sections consisting of Einstein metrics with positive scalar curvature.Comment: Minor changes, updated references. Final version. To appear in
Annales Henri Poincar | Singular Yamabe metrics and initial data with exactly
Kottler-Schwarzschild-de Sitter ends | singular yamabe metrics and initial data with exactly kottler-schwarzschild-de sitter ends | families einstein cosmological delaunay ends trivial coincide kottler schwarzschild sitter metrics infinite extent. purely riemannian geometric produces curvature metrics delaunay ends globally delaunay. ends gluing constructions. applies situations asymptotic spherical consisting einstein metrics minor updated references. version. annales henri poincar | non_dup | [] |
2600391 | 10.1007/s00023-008-0372-x | Consider the Schroedinger operator with semiclassical parameter h, in the
limit where h goes to zero. When the involved long-range potential is smooth,
it is well known that the boundary values of the operator's resolvent at a
positive energy E are bounded by O(1/h) if and only if the associated Hamilton
flow is non-trapping at energy E. In the present paper, we extend this result
to the case where the potential may possess Coulomb singularities. Since the
Hamilton flow then is not complete in general, our analysis requires the use of
an appropriate regularization.Comment: 39 pages, no figures, corrected versio | Semiclassical resolvent estimates for Schroedinger operators with
Coulomb singularities | semiclassical resolvent estimates for schroedinger operators with coulomb singularities | schroedinger semiclassical goes zero. resolvent hamilton trapping extend possess coulomb singularities. hamilton pages corrected versio | non_dup | [] |
1940923 | 10.1007/s00023-008-0381-9 | We study the general structure of Fermi conformal nets of von Neumann
algebras on the circle, consider a class of topological representations, the
general representations, that we characterize as Neveu-Schwarz or Ramond
representations, in particular a Jones index can be associated with each of
them. We then consider a supersymmetric general representation associated with
a Fermi modular net and give a formula involving the Fredholm index of the
supercharge operator and the Jones index. We then consider the net associated
with the super-Virasoro algebra and discuss its structure. If the central
charge c belongs to the discrete series, this net is modular by the work of F.
Xu and we get an example where our setting is verified by considering the
Ramond irreducible representation with lowest weight c/24. We classify all the
irreducible Fermi extensions of any super-Virasoro net in the discrete series,
thus providing a classification of all superconformal nets with central charge
less than 3/2.Comment: 49 pages. Section 8 has been removed. More details concerning the
diffeomorphism covariance are give | Structure and Classification of Superconformal Nets | structure and classification of superconformal nets | fermi conformal nets neumann algebras circle topological representations representations characterize neveu schwarz ramond representations jones them. supersymmetric fermi modular involving fredholm supercharge jones index. super virasoro structure. belongs modular verified ramond irreducible classify irreducible fermi extensions super virasoro superconformal nets pages. removed. concerning diffeomorphism covariance | non_dup | [] |
2558544 | 10.1007/s00023-008-0382-8 | Devices exhibiting the integer quantum Hall effect can be modeled by
one-electron Schroedinger operators describing the planar motion of an electron
in a perpendicular, constant magnetic field, and under the influence of an
electrostatic potential. The electron motion is confined to bounded or
unbounded subsets of the plane by confining potential barriers. The edges of
the confining potential barriers create edge currents. This is the second of
two papers in which we review recent progress and prove explicit lower bounds
on the edge currents associated with one- and two-edge geometries. In this
paper, we study various unbounded and bounded, two-edge geometries with soft
and hard confining potentials. These two-edge geometries describe the electron
confined to unbounded regions in the plane, such as a strip, or to bounded
regions, such as a finite length cylinder. We prove that the edge currents are
stable under various perturbations, provided they are suitably small relative
to the magnetic field strength, including perturbations by random potentials.
The existence of, and the estimates on, the edge currents are independent of
the spectral type of the operator.Comment: 57 page | Edge Currents for Quantum Hall Systems, II. Two-Edge, Bounded and
Unbounded Geometries | edge currents for quantum hall systems, ii. two-edge, bounded and unbounded geometries | devices exhibiting integer hall modeled schroedinger describing planar perpendicular electrostatic potential. confined unbounded subsets confining barriers. confining barriers create currents. papers progress bounds currents geometries. unbounded geometries confining potentials. geometries confined unbounded strip cylinder. currents perturbations suitably perturbations potentials. currents | non_dup | [] |
84091729 | 10.1007/s00023-008-0383-7 | We analyze a general class of self-adjoint difference operators
$H_\varepsilon = T_\varepsilon + V_\varepsilon$ on
$\ell^2(\varepsilon\mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well
potential and $\varepsilon$ is a small parameter. We construct a Finslerian
distance $d$ induced by $H_\varepsilon$ and show that short integral curves are
geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with
a rate controlled by the Finsler distance to the well. This is analog to
semiclassical Agmon estimates for Schr\"odinger operators.Comment: 27 page | Agmon-Type Estimates for a Class of Difference Operators | agmon-type estimates for a class of difference operators | analyze adjoint varepsilon varepsilon varepsilon varepsilon mathbb varepsilon varepsilon parameter. finslerian varepsilon geodesics. dirichlet eigenfunctions exponentially finsler well. analog semiclassical agmon schr odinger | non_dup | [] |
2435750 | 10.1007/s00023-008-0385-5 | We give conditions on a general stress-energy tensor T_{\alpha \beta} in a
spherically symmetric black hole spacetime which are sufficient to guarantee
that the black hole will contain a (spherically symmetric) marginally trapped
tube which is eventually achronal, connected, and asymptotic to the event
horizon. Price law decay per se is not required for this asymptotic result, and
in this general setting, such decay only implies that the marginally trapped
tube has finite length with respect to the induced metric. We do, however,
impose a smallness condition (B1) which one may obtain in practice by imposing
decay on the T_{vv} component of the stress-energy tensor. We give two
applications of the theorem to self-gravitating Higgs field spacetimes, one
using weak Price law decay, the other certain strong smallness and monotonicity
assumptions.Comment: 43 pages, 7 figures. Updated to agree with published version; Theorem
1 strengthened slightly, minor issues fixe | Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes | asymptotic behavior of spherically symmetric marginally trapped tubes | alpha beta spherically spacetime guarantee spherically marginally trapped tube eventually achronal asymptotic horizon. asymptotic marginally trapped tube metric. impose smallness imposing tensor. gravitating spacetimes smallness monotonicity pages figures. updated agree strengthened minor fixe | non_dup | [] |
2029971 | 10.1007/s00023-009-0007-x | In this paper we tackle the problem of constructing explicit examples of
topological cocycles of Roberts' net cohomology, as defined abstractly by
Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum
field theory on the two dimensional Einstein cylinder. After deriving some
crucial results of the algebraic framework of quantization, we address the
problem of the construction of the topological cocycles. All constructed
cocycles lead to unitarily equivalent representations of the fundamental group
of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).
The construction is carried out using only Cauchy data and related net of local
algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references
added. Accepted for publication in Ann. Henri Poincare | Topological features of massive bosons on two dimensional Einstein
space-time | topological features of massive bosons on two dimensional einstein space-time | tackle constructing topological cocycles roberts cohomology abstractly brunetti ruzzi. massive bosonic einstein cylinder. deriving crucial algebraic quantization topological cocycles. cocycles unitarily representations circle diffeomorphic cauchy cauchy algebras pages title changed minor typos corrected added. publication ann. henri poincare | non_dup | [] |
2094525 | 10.1007/s00023-009-0019-6 | There are five known classes of lattice equations that hold in every infinite
dimensional Hilbert space underlying quantum systems: generalised
orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations.
We obtain a result which opens a possibility that the first two classes
coincide. We devise new algorithms to generate Mayet-Godowski equations that
allow us to prove that the fourth class properly includes the third. An open
problem related to the last class is answered. Finally, we show some new
results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 figure | Hilbert Lattice Equations | hilbert lattice equations | hold infinite hilbert generalised orthoarguesian mayet godowski mayet godowski mayet equations. opens coincide. devise mayet godowski fourth properly third. answered. godowski lattices characterising pages | non_dup | [] |
1955094 | 10.1007/s00023-009-0400-5 | Consider (for simplicity) two one-dimensional semi-infinite leads coupled to
a quantum well via time dependent point interactions. In the remote past the
system is decoupled, and each of its components is at thermal equilibrium. In
the remote future the system is fully coupled. We define and compute the non
equilibrium steady state (NESS) generated by this evolution. We show that when
restricted to the subspace of absolute continuity of the fully coupled system,
the state does not depend at all on the switching. Moreover, we show that the
stationary charge current has the same invariant property, and derive the
Landau-Lifschitz and Landauer-Buttiker formulas.Comment: 30 pages, submitte | The effect of time-dependent coupling on non-equilibrium steady states | the effect of time-dependent coupling on non-equilibrium steady states | simplicity infinite interactions. remote decoupled equilibrium. remote coupled. steady ness evolution. restricted subspace continuity switching. stationary derive landau lifschitz landauer buttiker pages submitte | non_dup | [] |
2530634 | 10.1007/s00023-009-0401-4 | We study dispersion relations in the noncommutative \phi^3 and Wess-Zumino
model in the Yang-Feldman formalism at one-loop order. Nonplanar graphs lead to
a distortion of the dispersion relation. We find that the strength of this
effect is moderate if the scale of noncommutativity is identified with the
Planck scale and parameters typical for a Higgs field are employed. The
contribution of the nonplanar graphs is calculated rigorously using the
framework of oscillatory integrals.Comment: 23 pages, 2 figures. v2: Minor corrections and changes in the
presentatio | Dispersion relations in the noncommutative \phi^3 and Wess-Zumino model
in the Yang-Feldman formalism | dispersion relations in the noncommutative \phi^3 and wess-zumino model in the yang-feldman formalism | noncommutative wess zumino feldman formalism order. nonplanar distortion relation. moderate noncommutativity planck employed. nonplanar rigorously oscillatory pages figures. minor presentatio | non_dup | [] |
2027646 | 10.1007/s00023-009-0412-1 | Let $\Omega$ be a bounded domain in $R^n$ with $C^2$-smooth boundary of
co-dimension 1, and let $H=-\Delta +V(x)$ be a Schr\"odinger operator on
$\Omega$ with potential V locally bounded. We seek the weakest conditions we
can find on the rate of growth of the potential V close to the boundary which
guarantee essential self-adjointness of H on $C_0^\infty(\Omega)$. As a special
case of an abstract condition, we add optimal logarithmic type corrections to
the known condition $V(x)\geq \frac{3}{4d(x)^2}$, where
$d(x)=dist(x,\partial\Omega)$. The constant 1 in front of each logarithmic term
in Theorem 2 is optimal. The proof is based on a refined Agmon exponential
estimate combined with a well known multidimensional Hardy inequality | On confining potentials and essential self-adjointness for Schr\"odinger
operators on bounded domains in R^n | on confining potentials and essential self-adjointness for schr\"odinger operators on bounded domains in r^n | omega delta schr odinger omega locally bounded. seek weakest guarantee adjointness infty omega logarithmic frac dist omega front logarithmic optimal. refined agmon exponential multidimensional hardy inequality | non_dup | [] |
2027798 | 10.1007/s00023-009-0421-0 | We study a toy model for "partially open" wave-mechanical system, like for
instance a dielectric micro-cavity, in the semiclassical limit where ray
dynamics is applicable. Our model is a quantized map on the 2-dimensional
torus, with an additional damping at each time step, resulting in a subunitary
propagator, or "damped quantum map". We obtain analogues of Weyl's laws for
such maps in the semiclassical limit, and draw some more precise estimates when
the classical dynamic is chaotic.Comment: 35 pages, 5 figures. Corrected typos. Some proofs clarifie | Weyl laws for partially open quantum maps | weyl laws for partially open quantum maps | partially dielectric micro cavity semiclassical applicable. quantized torus damping subunitary propagator damped analogues weyl laws semiclassical draw precise pages figures. corrected typos. proofs clarifie | non_dup | [] |
2073996 | 10.1007/s00023-010-0021-z | We analyze the time evolution describing a quantum source for noninteracting
particles, either bosons or fermions. The growth behaviour of the particle
number (trace of the density matrix) is investigated, leading to spectral
criteria for sublinear or linear growth in the fermionic case, but also
establishing the possibility of exponential growth for bosons. We further study
the local convergence of the density matrix in the long time limit and prove
the semiclassical limit.Comment: 24 pages; In the new version, we added several references concerning
open quantum systems and present an extended result on linear particle
production in the fermionic cas | Dynamical phase transition for a quantum particle source | dynamical phase transition for a quantum particle source | analyze describing noninteracting bosons fermions. trace sublinear fermionic establishing exponential bosons. semiclassical pages concerning fermionic | non_dup | [] |
2072865 | 10.1007/s00023-010-0025-8 | We develop a gluing construction which adds scaled and truncated
asymptotically Euclidean solutions of the Einstein constraint equations to
compact solutions with potentially non-trivial cosmological constants. The
result is a one-parameter family of initial data which has ordinary and scaled
"point-particle" limits analogous to those of Gralla and Wald ("A rigorous
derivation of gravitational self-force," Class. Quantum Grav. 2008). In
particular, we produce examples of initial data which generalize Schwarzschild
- de Sitter initial data and gluing theorems of IMP-type | A Gluing Construction Regarding Point Particles in General Relativity | a gluing construction regarding point particles in general relativity | gluing adds scaled truncated asymptotically euclidean einstein potentially trivial cosmological constants. ordinary scaled analogous gralla wald rigorous derivation gravitational class. grav. generalize schwarzschild sitter gluing theorems | non_dup | [] |
2017048 | 10.1007/s00023-010-0027-6 | Let (g,K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold M
with non-positive Yamabe invariant (Y(M)). As noted by Fischer and Moncrief,
the reduced volume V(k)=(-k/3)^{3}Vol_{g(k)}(M) is monotonically decreasing in
the expanding direction and bounded below by V_{\inf}=(-1/6)Y(M))^{3/2}.
Inspired by this fact we define the ground state of the manifold M as "the
limit" of any sequence of CMC states {(g_{i},K_{i})} satisfying: i. k_{i}=-3,
ii. V_{i} --> V_{inf}, iii. Q_{0}((g_{i},K_{i}))< L where Q_{0} is the
Bel-Robinson energy and L is any arbitrary positive constant. We prove that (as
a geometric state) the ground state is equivalent to the Thurston
geometrization of M. Ground states classify naturally into three types. We
provide examples for each class, including a new ground state (the Double Cusp)
that we analyze in detail. Finally consider a long time and cosmologically
normalized flow (\g,\K)(s)=((-k/3)^{2}g,(-k/3))K) where s=-ln(-k) is in
[a,\infty). We prove that if E_{1}=E_{1}((\g,\K))< L (where E_{1}=Q_{0}+Q_{1},
is the sum of the zero and first order Bel-Robinson energies) the flow
(\g,\K)(s) persistently geometrizes the three-manifold M and the geometrization
is the ground state if V --> V_{inf}.Comment: 40 pages. This article is an improved version of the second part of
the First Version of arXiv:0705.307 | The ground state and the long-time evolution in the CMC Einstein flow | the ground state and the long-time evolution in the cmc einstein flow | einstein manifold yamabe fischer moncrief monotonically decreasing expanding inspired manifold satisfying iii. robinson constant. geometric thurston geometrization classify naturally types. cusp analyze detail. cosmologically infty robinson persistently geometrizes manifold geometrization .comment pages. | non_dup | [] |
2093491 | 10.1007/s00023-010-0031-x | The states in the irreducible modules of the minimal models can be
represented by infinite lattice paths arising from consideration of the
corresponding RSOS statistical models. For the M(p,2p+1) models, a completely
different path representation has been found recently, this one on a
half-integer lattice; it has no known underlying statistical-model
interpretation. The correctness of this alternative representation has not yet
been demonstrated, even at the level of the generating functions, since the
resulting fermionic characters differ from the known ones. This gap is filled
here, with the presentation of two versions of a bijection between the two path
representations of the M(p,2p+1) states.
In addition, a half-lattice path representation for the M(p+1,2p+1) models is
stated, and other generalisations suggested.Comment: 20 page | A bijection between paths for the M(p,2p+1) minimal model Virasoro
characters | a bijection between paths for the m(p,2p+1) minimal model virasoro characters | irreducible modules infinite paths arising consideration rsos models. integer interpretation. correctness generating fermionic characters ones. filled presentation versions bijection representations states. stated generalisations | non_dup | [] |
2087414 | 10.1007/s00023-010-0034-7 | Let T be an aperiodic and repetitive tiling of R^d with finite local
complexity. Let O be its tiling space with canonical transversal X. The tiling
equivalence relation R_X is the set of pairs of tilings in X which are
translates of each others, with a certain (etale) topology. In this paper R_X
is reconstructed as a generalized "tail equivalence" on a Bratteli diagram,
with its standard AF-relation as a subequivalence relation.
Using a generalization of the Anderson-Putnam complex, O is identified with
the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is
built from this sequence, and its set of infinite paths dB is homeomorphic to
X. The diagram B is endowed with a horizontal structure: additional edges that
encode the adjacencies of patches in T. This allows to define an etale
equivalence relation R_B on dB which is homeomorphic to R_X, and contains the
AF-relation of "tail equivalence".Comment: 34 pages, 4 figure | Tiling groupoids and Bratteli diagrams | tiling groupoids and bratteli diagrams | aperiodic repetitive tiling complexity. tiling canonical transversal tiling equivalence tilings translates etale topology. reconstructed tail equivalence bratteli subequivalence relation. generalization anderson putnam complexes. bratteli built infinite paths homeomorphic endowed encode adjacencies patches etale equivalence homeomorphic tail equivalence .comment pages | non_dup | [] |
2070981 | 10.1007/s00023-010-0037-4 | We consider a simple model of a cloud chamber consisting of a test particle
(the alpha-particle) interacting with two other particles (the atoms of the
vapour) subject to attractive potentials centered in $a_1, a_2 \in
\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing
spherical wave centered in the origin and the atoms are in their ground state.
We show that, under suitable assumptions on the physical parameters of the
system and up to second order in perturbation theory, the probability that both
atoms are ionized is negligible unless $a_2$ lies on the line joining the
origin with $a_1$. The work is a fully time-dependent version of the original
analysis proposed by Mott in 1929.Comment: 23 page | A time-dependent perturbative analysis for a quantum particle in a cloud
chamber | a time-dependent perturbative analysis for a quantum particle in a cloud chamber | chamber consisting alpha interacting vapour attractive potentials centered mathbb alpha outgoing spherical centered state. assumptions perturbation ionized negligible unless lies joining mott | non_dup | [] |
2128840 | 10.1007/s00023-010-0039-2 | The spherically symmetric Einstein-Vlasov system is considered in
Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem
is the issue of global existence for initial data without size restrictions.
The main purpose of the present work is to propose a method of approach for
general initial data, which improves the regularity of the terms that need to
be estimated compared to previous methods. We prove that global existence holds
outside the centre in both these coordinate systems. In the Schwarzschild case
we improve the bound on the momentum support obtained in \cite{RRS} for compact
initial data. The improvement implies that we can admit non-compact data with
both ingoing and outgoing matter. This extends one of the results in
\cite{AR1}. In particular our method avoids the difficult task of treating the
pointwise matter terms. Furthermore, we show that singularities never form in
Schwarzschild time for ingoing matter as long as $3m\leq r.$ This removes an
additional assumption made in \cite{A1}. Our result in maximal-isotropic
coordinates is analogous to the result in \cite{R1}, but our method is
different and it improves the regularity of the terms that need to be estimated
for proving global existence in general.Comment: 25 pages. To appear in Ann. Henri Poincar\' | Regularity results for the spherically symmetric Einstein-Vlasov system | regularity results for the spherically symmetric einstein-vlasov system | spherically einstein vlasov schwarzschild maximal isotropic coordinates. restrictions. propose improves regularity methods. coordinate systems. schwarzschild cite data. admit ingoing outgoing matter. extends cite avoids treating pointwise terms. singularities never schwarzschild ingoing removes cite maximal isotropic analogous cite improves regularity proving pages. ann. henri poincar | non_dup | [] |
2095966 | 10.1007/s00023-010-0041-8 | The purpose of this paper is to establish meromorphy properties of the
partial scattering amplitude T(lambda,k) associated with physically relevant
classes N_{w,alpha}^gamma of nonlocal potentials in corresponding domains
D_{gamma,alpha}^delta of the space C^2 of the complex angular momentum lambda
and of the complex momentum k (namely, the square root of the energy). The
general expression of T as a quotient Theta(lambda,k)/sigma(lambda,k) of two
holomorphic functions in D_{gamma,alpha}^delta is obtained by using the
Fredholm-Smithies theory for complex k, at first for lambda=l integer, and in a
second step for lambda complex (Real(lambda)>-1/2). Finally, we justify the
"Watson resummation" of the partial wave amplitudes in an angular sector of the
lambda-plane in terms of the various components of the polar manifold of T with
equation sigma(lambda,k)=0. While integrating the basic Regge notion of
interpolation of resonances in the upper half-plane of lambda, this unified
representation of the singularities of T also provides an attractive possible
description of antiresonances in the lower half-plane of lambda. Such a
possibility, which is forbidden in the usual theory of local potentials,
represents an enriching alternative to the standard Breit-Wigner hard-sphere
picture of antiresonances.Comment: 85 pages, 2 figure | Nonlocal potentials and complex angular momentum theory | nonlocal potentials and complex angular momentum theory | establish meromorphy lambda physically alpha gamma nonlocal potentials gamma alpha delta lambda quotient theta lambda sigma lambda holomorphic gamma alpha delta fredholm smithies lambda integer lambda lambda justify watson resummation amplitudes lambda polar manifold sigma lambda integrating regge notion interpolation resonances lambda unified singularities attractive antiresonances lambda. forbidden usual potentials enriching breit wigner sphere picture pages | non_dup | [] |
2065452 | 10.1007/s00023-010-0043-6 | We prove that sufficiently regular solutions to the wave equation
$\Box_g\phi=0$ on the exterior of the Schwarzschild black hole obey the
estimates $|\phi|\leq C_\delta v_+^{-{3/2}+\delta}$ and $|\partial_t\phi|\leq
C_{\delta} v_+^{-2+\delta}$ on a compact region of $r$ and along the event
horizon. This is proved with the help of a new vector field commutator that is
analogous to the scaling vector field on Minkowski spacetime. This result
improves the known decay rates in the region of finite $r$ and along the event
horizon.Comment: Remarks and References Adde | Improved decay for solutions to the linear wave equation on a
Schwarzschild black hole | improved decay for solutions to the linear wave equation on a schwarzschild black hole | sufficiently exterior schwarzschild obey delta delta delta delta horizon. proved commutator analogous minkowski spacetime. improves remarks adde | non_dup | [] |
2110799 | 10.1007/s00023-010-0050-7 | Moving beyond the classical additive and multiplicative approaches, we
present an "exponential" method for perturbative renormalization. Using Dyson's
identity for Green's functions as well as the link between the Faa di Bruno
Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the
composition of formal power series is analyzed. Eventually, we argue that the
new method has several attractive features and encompasses the BPHZ method. The
latter can be seen as a special case of the new procedure for renormalization
scheme maps with the Rota-Baxter property. To our best knowledge, although very
natural from group-theoretical and physical points of view, several ideas
introduced in the present paper seem to be new (besides the exponential method,
let us mention the notions of counterfactors and of order n bare coupling
constants).Comment: revised version; accepted for publication in Annales Henri Poincar | Exponential renormalization | exponential renormalization | moving additive multiplicative exponential perturbative renormalization. dyson bruno hopf hopf algebras feynman formal analyzed. eventually argue attractive encompasses bphz method. renormalization rota baxter property. ideas seem besides exponential mention notions counterfactors bare .comment revised publication annales henri poincar | non_dup | [] |
39260788 | 10.1007/s00023-010-0051-6 | The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading term depends only on the classical effect from the scalar potential. To the contrary, the quantum effect appears when the decay of the single site potential is fast. The corresponding leading term is estimated and the leading order is determined. In the multidimensional cases, the leading order varies in different ways from the known results in the Poisson case. The same problem is considered for the negative potential. These estimates are applied to investigate the long time asymptotics of Wiener integrals associated with the random potentials | Classical and Quantum Behavior of the Integrated Density of States for a Randomly Perturbed Lattice | classical and quantum behavior of the integrated density of states for a randomly perturbed lattice | asymptotic randomly perturbed infimum investigated. slow. potential. contrary fast. determined. multidimensional varies ways poisson case. potential. asymptotics wiener integrals potentials | non_dup | [] |
2131587 | 10.1007/s00023-010-0052-5 | We study discrete alloy-type random Schr\"odinger operators on
$\ell^2(\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of
eigenvalues in an energy interval of finite box restrictions of these types of
operators. If the single site potential is compactly supported and the
distribution of the coupling constant is of bounded variation a Wegner estimate
holds. The bound is polynomial in the volume of the box and thus applicable as
an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10 | Wegner estimate for discrete alloy-type models | wegner estimate for discrete alloy-type models | alloy schr odinger mathbb wegner bounds eigenvalues restrictions operators. compactly wegner holds. applicable ingredient localisation multiscale publication ahp. | non_dup | [] |
2134694 | 10.1007/s00023-010-0053-4 | This paper continues the investigation of the Casimir effect with the use of
the algebraic formulation of quantum field theory in the initial value setting.
Basing on earlier papers by one of us (AH) we approximate the Dirichlet and
Neumann boundary conditions by simple interaction models whose nonlocality in
physical space is under strict control, but which at the same time are
admissible from the point of view of algebraic restrictions imposed on models
in the context of Casimir backreaction. The geometrical setting is that of the
original parallel plates. By scaling our models and taking appropriate limit we
approach the sharp boundary conditions in the limit. The global force is
analyzed in that limit. One finds in Neumann case that although the sharp
boundary interaction is recovered in the norm resolvent sense for each model
considered, the total force per area depends substantially on its choice and
diverges in the sharp boundary conditions limit. On the other hand the local
energy density outside the interaction region, which in the limit includes any
compact set outside the strict position of the plates, has a universal limit
corresponding to sharp conditions. This is what one should expect in general,
and the lack of this discrepancy in Dirichlet case is rather accidental. Our
discussion pins down its precise origin: the difference in the order in which
scaling limit and integration over the whole space is carried out.Comment: 32 pages, accepted for publication in Ann. H. Poincar | Global vs local Casimir effect | global vs local casimir effect | continues casimir algebraic formulation setting. basing papers approximate dirichlet neumann nonlocality strict admissible algebraic restrictions imposed casimir backreaction. geometrical plates. sharp limit. limit. finds neumann sharp recovered norm resolvent substantially diverges sharp limit. strict plates universal sharp conditions. discrepancy dirichlet accidental. pins precise pages publication ann. poincar | non_dup | [] |
2102226 | 10.1007/s00023-010-0056-1 | The Chalker Coddington quantum network percolation model is numerically
pertinent to the understanding of the delocalization transition of the quantum
Hall effect. We study the model restricted to a cylinder of perimeter 2M. We
prove firstly that the Lyapunov exponents are simple and in particular that the
localization length is finite; secondly that this implies spectral
localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov
exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the
Lyapunov spectrum and finiteness of the localization length are proven. To
appear in Annales Henri Poincar | Localization Properties of the Chalker-Coddington Model | localization properties of the chalker-coddington model | chalker coddington percolation numerically pertinent delocalization hall effect. restricted cylinder perimeter firstly lyapunov exponents localization secondly localization. thirdly thouless lyapunov exponent pages figure. simplicity lyapunov finiteness localization proven. annales henri poincar | non_dup | [] |
2111981 | 10.1007/s00023-010-0058-z | We compute the vacuum expectation values of torus knot operators in
Chern-Simons theory, and we obtain explicit formulae for all classical gauge
groups and for arbitrary representations. We reproduce a known formula for the
HOMFLY invariants of torus links and we obtain an analogous formula for
Kauffman invariants. We also derive a formula for cable knots. We use our
results to test a recently proposed conjecture that relates HOMFLY and Kauffman
invariants.Comment: 20 pages, 5 figures; v2: minor changes, version submitted to AHP. The
final publication is available at
http://www.springerlink.com/content/a2614232873l76h6 | Chern-Simons Invariants of Torus Links | chern-simons invariants of torus links | expectation torus knot chern simons formulae representations. reproduce homfly invariants torus links analogous kauffman invariants. derive cable knots. conjecture relates homfly kauffman pages minor submitted ahp. publication | non_dup | [] |
2116642 | 10.1007/s00023-010-0062-3 | The process of ionization of a hydrogen atom by a short infrared laser pulse
is studied in the regime of very large pulse intensity, in the dipole
approximation. Let $A$ denote the integral of the electric field of the pulse
over time at the location of the atomic nucleus. It is shown that, in the limit
where $|A| \to \infty$, the ionization probability approaches unity and the
electron is ejected into a cone opening in the direction of $-A$ and of
arbitrarily small opening angle. Asymptotics of various physical quantities in
$|A|^{-1}$ is studied carefully. Our results are in qualitative agreement with
experimental data reported in \cite{1,2}.Comment: 27 pages, 1 figure | Ionization of Atoms by Intense Laser Pulses | ionization of atoms by intense laser pulses | ionization atom infrared dipole approximation. nucleus. infty ionization unity ejected cone opening arbitrarily opening angle. asymptotics quantities carefully. qualitative cite .comment pages | non_dup | [] |
2121598 | 10.1007/s00023-010-0063-2 | This article contains a detailed and rigorous proof of the construction of a
geometric invariant for initial data sets for the Einstein vacuum field
equations. This geometric invariant vanishes if and only if the initial data
set corresponds to data for the Kerr spacetime, and thus, it characterises this
type of data. The construction presented is valid for boosted and non-boosted
initial data sets which are, in a sense, asymptotically Schwarzschildean. As a
preliminary step to the construction of the geometric invariant, an analysis of
a characterisation of the Kerr spacetime in terms of Killing spinors is carried
out. A space spinor split of the (spacetime) Killing spinor equation is
performed, to obtain a set of three conditions ensuring the existence of a
Killing spinor of the development of the initial data set. In order to
construct the geometric invariant, we introduce the notion of approximate
Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the
initial hypersurface and satisfy a certain second order elliptic equation
---the approximate Killing spinor equation. This equation arises as the
Euler-Lagrange equation of a non-negative integral functional. This functional
constitutes part of our geometric invariant ---however, the whole functional
does not come from a variational principle. The asymptotic behaviour of
solutions to the approximate Killing spinor equation is studied and an
existence theorem is presented.Comment: 36 pages. Updated references. Technical details correcte | On the construction of a geometric invariant measuring the deviation
from Kerr data | on the construction of a geometric invariant measuring the deviation from kerr data | rigorous geometric einstein equations. geometric vanishes kerr spacetime characterises data. valid boosted boosted asymptotically schwarzschildean. preliminary geometric characterisation kerr spacetime killing spinors out. spinor split spacetime killing spinor ensuring killing spinor set. geometric notion approximate killing spinors. spinors valence spinors intrinsic hypersurface satisfy elliptic approximate killing spinor equation. arises euler lagrange functional. constitutes geometric come variational principle. asymptotic approximate killing spinor pages. updated references. correcte | non_dup | [] |
2151779 | 10.1007/s00023-010-0065-0 | We consider a waveguide modeled by the Laplacian in a straight planar strip.
The Dirichlet boundary condition is taken on the upper boundary, while on the
lower boundary we impose periodically alternating Dirichlet and Neumann
condition assuming the period of alternation to be small. We study the case
when the homogenization gives the Neumann condition instead of the alternating
ones. We establish the uniform resolvent convergence and the estimates for the
rate of convergence. It is shown that the rate of the convergence can be
improved by employing a special boundary corrector. Other results are the
uniform resolvent convergence for the operator on the cell of periodicity
obtained by the Floquet-Bloch decomposition, the two-terms asymptotics for the
band functions, and the complete asymptotic expansion for the bottom of the
spectrum with an exponentially small error term | On a waveguide with frequently alternating boundary conditions:
homogenized Neumann condition | on a waveguide with frequently alternating boundary conditions: homogenized neumann condition | waveguide modeled laplacian straight planar strip. dirichlet impose periodically alternating dirichlet neumann alternation small. homogenization neumann alternating ones. establish resolvent convergence. employing corrector. resolvent periodicity floquet bloch decomposition asymptotics asymptotic exponentially | non_dup | [] |
2099289 | 10.1007/s00023-010-0066-z | We show that, in a model where a non-relativistic particle is coupled to a
quantized relativistic scalar Bose field, the embedded mass shell of the
particle dissolves in the continuum when the interaction is turned on, provided
the coupling constant is sufficiently small. More precisely, under the
assumption that the fiber eigenvectors corresponding to the putative mass shell
are differentiable as functions of the total momentum of the system, we show
that a mass shell could exist only at a strictly positive distance from the
unperturbed embedded mass shell near the boundary of the energy-momentum
spectrum.Comment: Revised version: a remark added at the end of Section | Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction | absence of embedded mass shells: cerenkov radiation and quantum friction | relativistic quantized relativistic bose embedded dissolves continuum turned sufficiently small. precisely fiber eigenvectors putative differentiable strictly unperturbed embedded revised remark | non_dup | [] |
2141754 | 10.1007/s00023-010-0067-y | Quasi one-dimensional systems are systems of particles in domains which are
of infinite extent in one direction and of uniformly bounded size in all other
directions, e.g. on a cylinder of infinite length. The main result proven here
is that for such particle systems with Coulomb interactions and neutralizing
background, the so-called "jellium", at any temperature and at any finite-strip
width there is translation symmetry breaking. This extends the previous result
on Laughlin states in thin, two-dimensional strips by Jansen, Lieb and Seiler
(2009). The structural argument which is used here bypasses the question of
whether the translation symmetry breaking is manifest already at the level of
the one particle density function. It is akin to that employed by Aizenman and
Martin (1980) for a similar statement concerning symmetry breaking at all
temperatures in strictly one-dimensional Coulomb systems. The extension is
enabled through bounds which establish tightness of finite-volume charge
fluctuations.Comment: 26 pages, 6 figure | Symmetry breaking in quasi-1D Coulomb systems | symmetry breaking in quasi-1d coulomb systems | quasi infinite uniformly directions e.g. cylinder infinite length. proven coulomb neutralizing jellium strip translation breaking. extends laughlin strips jansen lieb seiler argument bypasses translation breaking manifest function. akin aizenman martin statement concerning breaking strictly coulomb systems. enabled bounds establish tightness pages | non_dup | [] |
2116719 | 10.1007/s00023-010-0069-9 | In this paper, we consider massless Dirac fields propagating in the outer
region of de Sitter-Reissner-Nordstr\"om black holes. We show that the metric
of such black holes is uniquely determined by the partial knowledge of the
corresponding scattering matrix $S(\lambda)$ at a fixed energy $\lambda \ne 0$.
More precisely, we consider the partial wave scattering matrices $S(\lambda,n)$
(here $\lambda \ne 0$ is the fixed energy and $n \in \N^*$ denotes the angular
momentum) defined as the restrictions of the full scattering matrix on a well
chosen basis of spin-weighted spherical harmonics. We prove that the mass $M$,
the square of the charge $Q^2$ and the cosmological constant $\Lambda$ of a
dS-RN black hole (and thus its metric) can be uniquely determined from the
knowledge of either the transmission coefficients $T(\lambda, n)$, or the
reflexion coefficients $R(\lambda, n)$ (resp. $L(\lambda, n)$), for all $n \in
{\mathcal{L}}$ where $\mathcal{L}$ is a subset of $\N^*$ that satisfies the
M\"untz condition $\sum_{n \in {\mathcal{L}}} \frac{1}{n} = +\infty$. Our main
tool consists in complexifying the angular momentum $n$ and in studying the
analytic properties of the "unphysical" scattering matrix $S(\lambda,z)$ in the
complex variable $z$. We show in particular that the quantities
$\frac{1}{T(\lambda,z)}$, $\frac{R(\lambda,z)}{T(\lambda,z)}$ and
$\frac{L(\lambda,z)}{T(\lambda,z)}$ belong to the Nevanlinna class in the
region $\{z \in \C, \ Re(z) >0 \}$ for which we have analytic uniqueness
theorems at our disposal. Eventually, as a by-product of our method, we obtain
reconstrution formulae for the surface gravities of the event and cosmological
horizons of the black hole which have an important physical meaning in the
Hawking effect.Comment: 40 page | Inverse scattering at fixed energy in de Sitter-Reissner-Nordstr\"om
black holes | inverse scattering at fixed energy in de sitter-reissner-nordstr\"om black holes | massless dirac propagating outer sitter reissner nordstr holes. holes uniquely lambda lambda precisely lambda lambda restrictions weighted spherical harmonics. cosmological lambda uniquely lambda reflexion lambda resp. lambda mathcal mathcal satisfies untz mathcal frac infty complexifying studying analytic unphysical lambda quantities frac lambda frac lambda lambda frac lambda lambda belong nevanlinna analytic uniqueness theorems disposal. eventually reconstrution formulae gravities cosmological horizons meaning hawking | non_dup | [] |
2145062 | 10.1007/s00023-010-0070-3 | We consider asymptotically flat Riemannian manifolds with nonnegative scalar
curvature that are conformal to $\R^{n}\setminus \Omega, n\ge 3$, and so that
their boundary is a minimal hypersurface. (Here, $\Omega\subset \R^{n}$ is open
bounded with smooth mean-convex boundary.) We prove that the ADM mass of any
such manifold is bounded below by $(V/\beta_{n})^{(n-2)/n}$, where $V$ is the
Euclidean volume of $\Omega$ and $\beta_{n}$ is the volume of the Euclidean
unit $n$-ball. This gives a partial proof to a conjecture of Bray and Iga
\cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.Comment: 7 page | A volumetric Penrose inequality for conformally flat manifolds | a volumetric penrose inequality for conformally flat manifolds | asymptotically riemannian manifolds nonnegative curvature conformal setminus omega hypersurface. omega convex boundary. manifold beta euclidean omega beta euclidean ball. conjecture bray cite brayiga surprisingly | non_dup | [] |
2149107 | 10.1007/s00023-010-0072-1 | In this paper we employ a novel technique combining the Euler Maclaurin
formula with the saddle point approximation method to obtain the asymptotic
behavior (in the limit of large representation index $J$) of generic Wigner
matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic
formulae for the character $\chi^J(g)$ of an SU(2) group element and for
Wigner's $3j$ symbol. Surprisingly, given that we perform five successive
layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is
in fact exact. This result provides a non trivial example of a
Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure | Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, $3j$ Symbols,
and Character Localization | asymptotes in su(2) recoupling theory: wigner matrices, $3j$ symbols, and character localization | employ combining euler maclaurin saddle asymptotic generic wigner derive asymptotic formulae character wigner symbol. surprisingly successive approximations asymptotic exact. trivial duistermaat heckman localization pages | non_dup | [] |
2126202 | 10.1007/s00023-010-0074-z | In axial symmetry, there is a gauge for Einstein equations such that the
total mass of the spacetime can be written as a conserved, positive definite,
integral on the spacelike slices. This property is expected to play an
important role in the global evolution. In this gauge the equations reduce to a
coupled hyperbolic-elliptic system which is formally singular at the axis. Due
to the rather peculiar properties of the system, the local in time existence
has proved to resist analysis by standard methods. To analyze the principal
part of the equations, which may represent the main source of the difficulties,
we study linear perturbation around the flat Minkowski solution in this gauge.
In this article we solve this linearized system explicitly in terms of integral
transformations in a remarkable simple form. This representation is well suited
to obtain useful estimates to apply in the non-linear case.Comment: 13 pages. We suppressed the statements about decay at infinity. The
proofs of these statements were incomplete. The complete proofs will require
extensive technical analysis. We will studied this in a subsequent work. We
also have rewritten the introduction and slighted changed the titl | Linear perturbations for the vacuum axisymmetric Einstein equations | linear perturbations for the vacuum axisymmetric einstein equations | axial einstein spacetime conserved definite spacelike slices. evolution. hyperbolic elliptic formally singular axis. peculiar proved resist methods. analyze principal difficulties perturbation minkowski gauge. solve linearized explicitly transformations remarkable form. suited pages. suppressed statements infinity. proofs statements incomplete. proofs extensive analysis. work. rewritten slighted changed titl | non_dup | [] |
2131059 | 10.1007/s00023-011-0076-5 | We derive explicit formulae for a set of constraints for the Einstein
equations on a null hypersurface, in arbitrary dimensions. We solve these
constraints and show that they provide necessary and sufficient conditions so
that a spacetime solution of the Cauchy problem on a characteristic cone for
the hyperbolic system of the reduced Einstein equations in wave-map gauge also
satisfies the full Einstein equations. We prove a geometric uniqueness theorem
for this Cauchy problem in the vacuum case.Comment: 83 pages, 1 figur | The Cauchy problem on a characteristic cone for the Einstein equations
in arbitrary dimensions | the cauchy problem on a characteristic cone for the einstein equations in arbitrary dimensions | derive formulae einstein hypersurface dimensions. solve spacetime cauchy cone hyperbolic einstein satisfies einstein equations. geometric uniqueness cauchy pages figur | non_dup | [] |
2104562 | 10.1007/s00023-011-0079-2 | We place further restriction on the possible topology of stationary
asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that
the horizon manifold can be either a connected sum of Lens spaces and "handles"
$S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of
isometries (with no "handles"). The resulting horizon topologies include Prism
manifolds and quotients of the Poincare homology sphere. We also show that the
topology of the domain of outer communication is a cartesian product of the
time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s
and $CP^2$'s, minus the black hole itself. We do not assume the existence of
any Killing vector beside the asymptotically timelike one required by
definition for stationarity.Comment: LaTex, 22 pages, 9 figure | Further restrictions on the topology of stationary black holes in five
dimensions | further restrictions on the topology of stationary black holes in five dimensions | restriction topology stationary asymptotically holes spacetime dimensions. horizon manifold lens handles quotient isometries handles horizon topologies prism manifolds quotients poincare homology sphere. topology outer cartesian mathbb minus itself. killing beside asymptotically timelike latex pages | non_dup | [] |
2150295 | 10.1007/s00023-011-0080-9 | Explicit Fermi coordinates are given for geodesic observers comoving with the
Hubble flow in expanding Robertson-Walker spacetimes, along with exact
expressions for the metric tensors in Fermi coordinates. For the case of non
inflationary cosmologies, it is shown that Fermi coordinate charts are global,
and space-time is foliated by space slices of constant Fermi (proper) time that
have finite extent. A universal upper bound for the proper radius of any leaf
of the foliation, i.e., for the proper radius of the spatial universe at any
fixed time of the geodesic observer, is given. A general expression is derived
for the geometrically defined Fermi relative velocity of a test particle (e.g.
a galaxy) comoving with the Hubble flow away from the observer. Least upper
bounds of superluminal recessional Fermi velocities are given for spacetimes
whose scale factors follow power laws, including matter-dominated and
radiation-dominated cosmologies. Exact expressions for the proper radius of any
leaf of the foliation for this same class of spacetimes are given. It is shown
that the radii increase linearly with proper time of the observer moving with
the Hubble flow. These results are applied to particular cosmological models.Comment: This revised version corrects minor typo | Fermi coordinates, simultaneity, and expanding space in Robertson-Walker
cosmologies | fermi coordinates, simultaneity, and expanding space in robertson-walker cosmologies | fermi geodesic observers comoving hubble expanding robertson walker spacetimes expressions tensors fermi coordinates. inflationary cosmologies fermi coordinate charts foliated slices fermi proper extent. universal proper leaf foliation i.e. proper universe geodesic observer given. geometrically fermi e.g. comoving hubble away observer. bounds superluminal recessional fermi velocities spacetimes laws dominated dominated cosmologies. expressions proper leaf foliation spacetimes given. radii linearly proper observer moving hubble flow. cosmological revised corrects minor typo | non_dup | [] |
2139681 | 10.1007/s00023-011-0082-7 | The recent "breakdown criterion" result of S. Klainerman and I. Rodnianski
stated roughly that an Einstein-vacuum spacetime, given as a CMC foliation, can
be further extended in time if the second fundamental form and the derivative
of the lapse of the foliation are uniformly bounded. This theorem and its proof
were extended to Einstein-scalar and Einstein-Maxwell spacetimes in the
author's Ph.D. thesis. In this paper, we state the main results of the thesis,
and we summarize and discuss their proofs. In particular, we will discuss the
various issues resulting from nontrivial Ricci curvature and the coupling
between the Einstein and the field equations.Comment: 62 pages This version: corrected minor typos, expanded Section 6
(geometry of null cones | On Breakdown Criteria for Nonvacuum Einstein Equations | on breakdown criteria for nonvacuum einstein equations | breakdown criterion klainerman rodnianski stated roughly einstein spacetime foliation lapse foliation uniformly bounded. einstein einstein maxwell spacetimes ph.d. thesis. thesis summarize proofs. nontrivial ricci curvature einstein pages corrected minor typos expanded cones | non_dup | [] |
2121396 | 10.1007/s00023-011-0089-0 | Quantum field theory on the noncommutative two-dimensional Minkowski space
with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a
continuous set of generalised eigenfunctions of the wave operator, and directly
in position space. In both settings, we find a new type of divergence in planar
graphs. It is present at and above the self-dual point. This new kind of
divergence might make the construction of a Minkowski space version of the
Grosse-Wulkenhaar model impossible.Comment: 26 pages, published versio | Divergences in quantum field theory on the noncommutative
two-dimensional Minkowski space with Grosse-Wulkenhaar potential | divergences in quantum field theory on the noncommutative two-dimensional minkowski space with grosse-wulkenhaar potential | noncommutative minkowski grosse wulkenhaar ways generalised eigenfunctions space. settings divergence planar graphs. point. kind divergence minkowski grosse wulkenhaar pages versio | non_dup | [] |
2138600 | 10.1007/s00023-011-0090-7 | Motivated by recent work of Choquet-Bruhat, Chrusciel, and Martin-Garcia, we
prove monotonicity properties and comparison results for the area of slices of
the null cone of a point in a Lorentzian manifold. We also prove volume
comparison results for subsets of the null cone analogous to the Bishop-Gromov
relative volume monotonicity theorem and Guenther's volume comparison theorem.
We briefly discuss how these estimates may be used to control the null second
fundamental form of slices of the null cone in Ricci-flat Lorentzian
four-manifolds with null curvature bounded above.Comment: 16 pages, no figures. Typos fixed. One garbled proof corrected.
Published versio | Areas and volumes for null cones | areas and volumes for null cones | motivated choquet bruhat chrusciel martin garcia monotonicity slices cone lorentzian manifold. subsets cone analogous bishop gromov monotonicity guenther theorem. briefly slices cone ricci lorentzian manifolds curvature pages figures. typos fixed. garbled corrected. versio | non_dup | [] |
2115043 | 10.1007/s00023-011-0091-6 | We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory | Ground States in the Spin Boson Model | ground states in the spin boson model | describing linearly relativistic massless bosons boson admits lambda. analytic lambda analytic lambda. infrared regularization imposed. theoretic renormalization analysis. positivity argument boson unique. analytic perturbation | non_dup | [] |
2123643 | 10.1007/s00023-011-0093-4 | We investigate the edge conductance of particles submitted to an Iwatsuka
magnetic field, playing the role of a purely magnetic barrier. We also consider
magnetic guides generated by generalized Iwatsuka potentials. In both cases we
prove quantization of the edge conductance. Next, we consider magnetic
perturbations of such magnetic barriers or guides, and prove stability of the
quantized value of the edge conductance. Further, we establish a sum rule for
edge conductances. Regularization within the context of disordered systems is
discussed as well.Comment: 25 page | Quantization of edge currents along magnetic barriers and magnetic
guides | quantization of edge currents along magnetic barriers and magnetic guides | conductance submitted iwatsuka playing purely barrier. guides iwatsuka potentials. quantization conductance. perturbations barriers guides quantized conductance. establish conductances. regularization disordered | non_dup | [] |
2146071 | 10.1007/s00023-011-0094-3 | In this paper the existence of a class of self-similar solutions of the
Einstein-Vlasov system is proved. The initial data for these solutions are not
smooth, with their particle density being supported in a submanifold of
codimension one. They can be thought of as intermediate between smooth
solutions of the Einstein-Vlasov system and dust. The motivation for studying
them is to obtain insights into possible violation of weak cosmic censorship by
solutions of the Einstein-Vlasov system. By assuming a suitable form of the
unknowns it is shown that the existence question can be reduced to that of the
existence of a certain type of solution of a four-dimensional system of
ordinary differential equations depending on two parameters. This solution
starts at a particular point $P_0$ and converges to a stationary solution $P_1$
as the independent variable tends to infinity. The existence proof is based on
a shooting argument and involves relating the dynamics of solutions of the
four-dimensional system to that of solutions of certain two- and
three-dimensional systems obtained from it by limiting processes.Comment: 47 page | A class of dust-like self-similar solutions of the massless
Einstein-Vlasov system | a class of dust-like self-similar solutions of the massless einstein-vlasov system | einstein vlasov proved. submanifold codimension one. thought einstein vlasov dust. motivation studying insights violation cosmic censorship einstein vlasov system. unknowns ordinary parameters. starts converges stationary tends infinity. shooting argument involves relating limiting | non_dup | [] |
2143603 | 10.1007/s00023-011-0096-1 | We consider the non-relativistic Hartree model in the gravitational case,
i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct
stationary states with non-zero temperature by minimizing the corresponding
free energy functional. It is proved that minimizers exist if and only if the
temperature of the system is below a certain threshold(possibly infinite),
which itself depends on the specific choice of the entropy functional. We also
investigate whether the corresponding minimizers are mixed or pure quantum
states and characterize a positive critical temperature above which mixed
states appear | Thermal effects in gravitational Hartree systems | thermal effects in gravitational hartree systems | relativistic hartree gravitational i.e. attractive coulomb newton interaction. stationary minimizing functional. proved minimizers possibly infinite functional. minimizers characterize | non_dup | [] |
2114168 | 10.1007/s00023-011-0097-0 | In this paper, we prove the following theorem regarding the Wang-Yau
quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a
boundary component of some compact, time-symmetric, spacelike hypersurface
$\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy
condition. Suppose the induced metric on $\Sigma$ has positive Gaussian
curvature and all boundary components of $\Omega$ have positive mean curvature.
Suppose $H \le H_0$ where $H$ is the mean curvature of $\Sigma$ in $\Omega$ and
$H_0$ is the mean curvature of $\Sigma$ when isometrically embedded in $R^3$.
If $\Omega$ is not isometric to a domain in $R^3$, then 1. the Brown-York mass
of $\Sigma$ in $\Omega$ is a strict local minimum of the Wang-Yau quasi-local
energy of $\Sigma$, 2. on a small perturbation $\tilde{\Sigma}$ of $\Sigma$ in
$N$, there exists a critical point of the Wang-Yau quasi-local energy of
$\tilde{\Sigma}$.Comment: substantially revised, main theorem replaced, Section 3 adde | Critical points of Wang-Yau quasi-local energy | critical points of wang-yau quasi-local energy | quasi spacelike spacetime sigma spacelike hypersurface omega oriented spacetime satisfying condition. sigma curvature omega curvature. curvature sigma omega curvature sigma isometrically embedded omega isometric brown sigma omega strict quasi sigma perturbation tilde sigma sigma quasi tilde sigma .comment substantially revised replaced adde | non_dup | [] |
2125221 | 10.1007/s00023-011-0103-6 | We provide an explicit combinatorial expansion for the ground state energy of
the massless spin-Boson model as a power series in the coupling parameter. Our
method uses the technique of cluster expansion in constructive quantum field
theory and takes as a starting point the functional integral representation and
its reduction to an Ising model on the real line with long range interactions.
We prove the analyticity of our expansion and provide an explicit lower bound
on the radius of convergence. We do not need multiscale nor renormalization
group analysis. A connection to the loop-erased random walk is indicated.Comment: 32 pages, 4 figures, a remark and references added, typos corrected,
minor computational errors correcte | The Ground State Energy of The Massless Spin-Boson Model | the ground state energy of the massless spin-boson model | combinatorial massless boson parameter. constructive ising interactions. analyticity convergence. multiscale renormalization analysis. connection erased walk pages remark typos corrected minor correcte | non_dup | [] |