pinecone/core-2020-05-10-deduplication huggingface dataset:
Heat-Kernel Approach to UV/IR Mixing on Isospectral Deformation
  Manifolds

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
An extension principle for the Einstein-Vlasov system in spherical
  symmetry

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
Time delay and short-range scattering in quantum waveguides

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
A Characterization of Model Multi-colour Sets

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
On a characteristic initial value problem in Plasma physics

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
Quantum backreaction (Casimir) effect. II. Scalar and electromagnetic
  fields

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
Energetic and dynamic properties of a quantum particle in a spatially
  random magnetic field with constant correlations along one direction

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]
Quantum incompressibility and Razumov Stroganov type conjectures

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
A general resonance theory based on Mourre's inequality

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
Long time motion of NLS solitary waves in a confining potential

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
Topological Factors Derived From Bohmian Mechanics

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
Spectral convergence of non-compact quasi-one-dimensional spaces

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
Spacetime causality in the study of the Hankel transform

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
Upper bounds on the rate of quantum ergodicity

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
Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and
  open spin chains in any representation

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
On the R-matrix realization of Yangians and their representations

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
Exotic Bialgebra S03: Representations, Baxterisation and Applications

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
Bosonization and Vertex Algebras with Defects

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
The elliptic scattering theory of the 1/2-XYZ and higher order Deformed
  Virasoro Algebras

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 six-vertex model at roots of unity and some highest weight
  representations of the sl(2) loop algebra

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
Fusion of Baxter's Elliptic $R$-matrix and the Vertex-Face
  Correspondence

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
Mean-field theory for Heisenberg zigzag ladder: Ground state energy and
  spontaneous symmetry breaking

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
The two-site Bose--Hubbard model

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
Smoothness of Correlations in the Anderson Model at Strong Disorder

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
Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps

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
Lower bounds on the lowest spectral gap of singular potential
  Hamiltonians

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
The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin Transform Techniques

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
Patterson-Sullivan distributions and quantum ergodicity

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