pinecone/core-2020-05-10-deduplication huggingface dataset:
Quantum field theory on affine bundles

We develop a general framework for the quantization of bosonic and fermionic
field theories on affine bundles over arbitrary globally hyperbolic spacetimes.
All concepts and results are formulated using the language of category theory,
which allows us to prove that these models satisfy the principle of general
local covariance. Our analysis is a preparatory step towards a full-fledged
quantization scheme for the Maxwell field, which emphasises the affine bundle
structure of the bundle of principal U(1)-connections. As a by-product, our
construction provides a new class of exactly tractable locally covariant
quantum field theories, which are a mild generalization of the linear ones. We
also show the existence of a functorial assignment of linear quantum field
theories to affine ones. The identification of suitable algebra homomorphisms
enables us to induce whole families of physical states (satisfying the
microlocal spectrum condition) for affine quantum field theories by pulling
back quasi-free Hadamard states of the underlying linear theories.Comment: 34 pages, no figures; v2: 35 pages, compatible with version to be
  published in Annales Henri Poincar
Averaging Fluctuations in Resolvents of Random Band Matrices

We consider a general class of random matrices whose entries are centred
random variables, independent up to a symmetry constraint. We establish precise
high-probability bounds on the averages of arbitrary monomials in the resolvent
matrix entries. Our results generalize the previous results of [5,16,17] which
constituted a key step in the proof of the local semicircle law with optimal
error bound in mean-field random matrix models. Our bounds apply to random band
matrices, and improve previous estimates from order 2 to order 4 in the cases
relevant for applications. In particular, they lead to a proof of the diffusion
approximation for the magnitude of the resolvent of random band matrices. This,
in turn, implies new delocalization bounds on the eigenvectors. The
applications are presented in a separate paper [3]
Twisted equivariant matter

We show how general principles of symmetry in quantum mechanics lead to
twisted notions of a group representation. This framework generalizes both the
classical 3-fold way of real/complex/quaternionic representations as well as a
corresponding 10-fold way which has appeared in condensed matter and nuclear
physics. We establish a foundation for discussing continuous families of
quantum systems. Having done so, topological phases of quantum systems can be
defined as deformation classes of continuous families of gapped Hamiltonians.
For free particles there is an additional algebraic structure on the
deformation classes leading naturally to notions of twisted equivariant
K-theory. In systems with a lattice of translational symmetries we show that
there is a canonical twisting of the equivariant K-theory of the Brillouin
torus. We give precise mathematical definitions of two invariants of the
topological phases which have played an important role in the study of
topological insulators. Twisted equivariant K-theory provides a finer
classification of topological insulators than has been previously available.Comment: 93 pages, 1 figure; v2 has minor corrections and clarifications for
  publication in AH
Convexity of reduced energy and mass angular momentum inequalities

In this paper, we extend the work in
\cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic
conditions on the second fundamental form, and we also give an $L^{6}-$norm
bound for the difference between general data and Extreme Kerr data or Extreme
Kerr-Newman data by proving convexity of the renormalized Dirichlet energy when
the target has non-positive curvature. In particular, we give the first proof
of the strict mass/angular momentum/charge inequality for axisymmetric
Einstein/Maxwell data which is not identical with the extreme Kerr-Newman
solution.Comment: 27 page
On the eigenvalue spacing distribution for a point scatterer on the flat
  torus

We study the level spacing distribution for the spectrum of a point scatterer
on a flat torus. In the 2-dimensional case, we show that in the weak coupling
regime the eigenvalue spacing distribution coincides with that of the spectrum
of the Laplacian (ignoring multiplicties), by showing that the perturbed
eigenvalues generically clump with the unperturbed ones on the scale of the
mean level spacing. We also study the three dimensional case, where the
situation is very different.Comment: 25 page
Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices
  with Decaying Interaction

In this paper we consider lattice systems coupled by local interactions. We
prove invariant manifold theorems for whiskered tori (we recall that whiskered
tori are quasi-periodic solutions with exponentially contracting and expanding
directions in the linearized system). The invariant manifolds we construct
generalize the usual (strong) (un) stable manifolds and allow us to consider
also non-resonant manifolds. We show that if the whiskered tori are localized
near a collection of specific sites, then so are the invariant manifolds.
  We recall that the existence of localized whiskered tori has recently been
proven for symplectic maps and flows in Fontich et. al. (submitted), but our
results do not need that the systems are symplectic. For simplicity we will
present first the main results for maps, but we will show tha the result for
maps imply the results for flows. It is also true that the results for flows
can be proved directly following the same ideas.Comment: This version corrects a bibliographical typo that appears in the
  version published in Annales Henri Poincare: Reference [FdlLS12] was wrongly
  listed by the publisher as "submitted to Jour. Diff. Equ." in the published
  version. Reference [FdlLS12] has not been submitted to Jour. Diff. Eq
Explicit solution of the (quantum) elliptic Calogero-Sutherland model

We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
$q$ of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
  order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
  completely revised: the results of v1 and v2 are extended to all order
On a coordinate independent description of string worldsheet theory

We study worldsheet conformal invariance for bosonic string propagating in a
curved background using the hamiltonian formalism. In order to formulate the
problem in a background independent manner we first rewrite the worldsheet
theory in a language where it describes a single particle moving in an
infinite-dimensional curved spacetime. This language is developed at a formal
level without regularizing the infinite-dimensional traces. Then we adopt
DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of
quantum mechanics in the present context. Given the expressions for the
classical Virasoro generators, this procedure enables us to define the
coordinate invariant quantum analogues which we call DeWitt-Virasoro
generators. This framework also enables us to calculate the invariant matrix
elements of an arbitrary operator constructed out of the DeWitt-Virasoro
generators between two arbitrary scalar states. Using these tools we further
calculate the DeWitt-Virasoro algebra in spin-zero representation. The result
is given by the Witt algebra with additional anomalous terms that vanish for
Ricci-flat backgrounds. Further analysis need to be performed in order to
precisely relate this with the beta function computation of Friedan and others.
Finally, we explain how this analysis improves the understanding of showing
conformal invariance for certain pp-wave that has been recently discussed using
hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no
  change in conclusio
On applications of Orlicz spaces to statistical physics

We present a new rigorous approach based on Orlicz spaces for
the description of the statistics of large regular statistical systems, both
classical and quantum. The pair of Orlicz spaces we explicitly use are,
respectively, built on the exponential function (for the description of regular
observables) and on an entropic type function (for the corresponding
states). They form a dual pair (both for classical and quantum systems).
This pair has the advantage of being general enough to encompass regular
observables, and specific enough for the latter Orlicz space to select
states with a well-defined entropy function. Moreover for small quantum
systems, this pair is shown to agree with the classical pairing of bounded
linear operators on a Hilbert space, and the trace-class operators.Grant Number N N202 208238; Foundation
for Polish Science TEAM project cofinanced by the EU European Regional
Development Fund for W.A. Majewski; National Research
Foundation for L.E. Labuschagnehttp://dx.doi.org/10.1007/s00023-013-0267-3http://www.springer.com/birkhauser/physics/journal/2
Local exclusion and Lieb-Thirring inequalities for intermediate and
  fractional statistics

In one and two spatial dimensions there is a logical possibility for
identical quantum particles different from bosons and fermions, obeying
intermediate or fractional (anyon) statistics. We consider applications of a
recent Lieb-Thirring inequality for anyons in two dimensions, and derive new
Lieb-Thirring inequalities for intermediate statistics in one dimension with
implications for models of Lieb-Liniger and Calogero-Sutherland type. These
inequalities follow from a local form of the exclusion principle valid for such
generalized exchange statistics.Comment: Revised and accepted version. 49 pages, 2 figure
A class of conformal curves in the Reissner-Nordstr\"om spacetime

A class of curves with special conformal properties (conformal curves) is
studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data
for the conformal curves can be prescribed so that the resulting congruence of
curves extends smoothly to future and past null infinity. The formation of
conjugate points on these congruences is examined. The results of this analysis
are expected to be of relevance for the discussion of the Reissner-Nordstr\"om
spacetime as a solution to the conformal field equations and for the global
numerical evaluation of static black hole spacetimes.Comment: 32 pages, 2 figure
On second variation of Wang-Yau quasi-local energy

We study a functional on the boundary of a compact Riemannian 3-manifold of
nonnegative scalar curvature. The functional arises as the second variation of
the Wang-Yau quasi-local energy in general relativity. We prove that the
functional is positive definite on large coordinate spheres, and more general
on nearly round surfaces including large constant mean curvature spheres in
asymptotically flat 3-manifolds with positive mass; it is also positive
definite on small geodesics spheres, whose centers do not have vanishing
curvature, in Riemannian 3-manifolds of nonnegative scalar curvature. We also
give examples of functions H, which can be made arbitrarily close to the
constant 2, on the standard sphere such that the boundary data consisting of
the standard spherical metric and H has positive Brown-York mass while the
associated functional is negative somewhere.Comment: 36 page
The Reduced Hartree-Fock Model for Short-Range Quantum Crystals with Nonlocal Defects

International audienceIn this article, we consider quantum crystals with defects in the reduced Hartree-Fock framework. The nuclei are supposed to be classical particles arranged around a reference periodic configuration. The perturbation is assumed to be small in amplitude, but need not be localized in a specific region of space or have any spatial invariance. Assuming Yukawa interactions, we prove the existence of an electronic ground state, solution of the self-consistent field equation. Next, by studying precisely the decay properties of this solution for local defects, we are able to expand the density of states of the nonlinear Hamiltonian of a system with a random perturbation of Anderson-Bernoulli type, in the limit of low concentration of defects. One important step in the proof of our results is the analysis of the dielectric response of the crystal to an effective charge perturbation
A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian

We consider the Landau Hamiltonian perturbed by a long-range electric
potential $V$. The spectrum of the perturbed operator consists of eigenvalue
clusters which accumulate to the Landau levels. First, we obtain an estimate of
the rate of the shrinking of these clusters to the Landau levels as the number
of the cluster $q$ tends to infinity. Further, we assume that there exists an
appropriate $\V$, homogeneous of order $-\rho$ with $\rho \in (0,1)$, such that
$V(x) = \V(x) + O(|x|^{-\rho - \epsilon})$, $\epsilon > 0$, as $|x| \to
\infty$, and investigate the asymptotic distribution of the eigenvalues within
a given cluster, as $q \to \infty$. We obtain an explicit description of the
asymptotic density of the eigenvalues in terms of the mean-value transform of
$\V$.Comment: 27 pages, to appear in Ann. H Poincar\'
Anderson's Orthogonality Catastrophe for One-dimensional Systems

We derive rigorously the leading asymptotics of the so-called Anderson
integral in the thermodynamic limit for one-dimensional, non-relativistic,
spin-less Fermi systems. The coefficient, $\gamma$, of the leading term is
computed in terms of the S-matrix. This implies a lower and an upper bound on
the exponent in Anderson's orthogonality catastrophe, $\tilde
CN^{-\tilde\gamma}\leq \mathcal{D}_N\leq CN^{-\gamma}$ pertaining to the
overlap, $\mathcal{D}_N$, of ground states of non-interacting fermions.Comment: 39 page
Graphical Calculus for the Double Affine Q-Dependent Braid Group

We define a double affine $Q$-dependent braid group. This group is
constructed by appending to the braid group a set of operators $Q_i$, before
extending it to an affine $Q$-dependent braid group. We show specifically that
the elliptic braid group and the double affine Hecke algebra (DAHA) can be
obtained as quotient groups. Complementing this we present a pictorial
representation of the double affine $Q$-dependent braid group based on ribbons
living in a toroid. We show that in this pictorial representation we can fully
describe any DAHA. Specifically, we graphically describe the parameter $q$ upon
which this algebra is dependent and show that in this particular representation
$q$ corresponds to a twist in the ribbon
Semiclassics for particles with spin via a Wigner-Weyl-type calculus

We show how to relate the full quantum dynamics of a spin-1/2 particle on R^d
to a classical Hamiltonian dynamics on the enlarged phase space R^d x S^2 up to
errors of second order in the semiclassical parameter. This is done via an
Egorov-type theorem for normal Wigner-Weyl calculus for R^d [Lei10,Fol89]
combined with the Stratonovich-Weyl calculus for SU(2) [VGB89]. For a specific
class of Hamiltonians, including the Rabi- and Jaynes-Cummings model, we prove
an Egorov theorem for times much longer than the semiclassical time scale. We
illustrate the approach for a simple model of the Stern-Gerlach experiment.Comment: 24 page
Geometry of normal graphs in Euclidean space and applications to the
  Penrose inequality in Minkowski

The Penrose inequality in Minkowski is a geometric inequality relating the
total outer null expansion and the area of closed, connected and spacelike
codimension-two surfaces S in the Minkowski spacetime, subject to an additional
convexity assumption. In a recent paper, Brendle and Wang find a sufficient
condition for the validity of this Penrose inequality in terms of the geometry
of the orthogonal projection of S onto a constant time hyperplane. In this
work, we study the geometry of hypersurfaces in n-dimensional euclidean space
which are normal graphs over other surfaces and relate the intrinsic and
extrinsic geometry of the graph with that of the base hypersurface. These
results are used to rewrite Brendle and Wang's condition explicitly in terms of
the time height function of S over a hyperplane and the geometry of the
projection of S along its past null cone onto this hyperplane. We also include,
in an Appendix, a self-contained summary of known and new results on the
geometry of projections along the Killing direction of codimension
two-spacelike surfaces in a strictly static spacetime.Comment: 15 pages, 1 figure, Late
Magnetic effects in curved quantum waveguides

28 pagesInternational audienceThe interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive effective, lower-dimensional models which depend on the intensity of the magnetic field and curvatures. The results are used to establish complete asymptotic expansions for eigenvalues. Spectral stability properties based on Hardy-type inequalities induced by magnetic fields are also analysed
Excitation spectrum of interacting bosons in the mean-field
  infinite-volume limit

We consider homogeneous Bose gas in a large cubic box with periodic boundary
conditions, at zero temperature. We analyze its excitation spectrum in a
certain kind of a mean field infinite volume limit. We prove that under
appropriate conditions the excitation spectrum has the form predicted by the
Bogoliubov approximation. Our result can be viewed as an extension of the
result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes.Comment: Revised and extended version. 26 pages, 4 figures. To appear in
  Annales Henri Poincar\'
The scaling and mass expansion

The scaling and mass expansion (shortly 'sm-expansion') is a new axiom for
causal perturbation theory, which is a stronger version of a frequently used
renormalization condition in terms of Steinmann's scaling degree. If one
quantizes the underlying free theory by using a Hadamard function (which is
smooth in $m\geq 0$), one can reduce renormalization of a massive model to the
extension of a minimal set of mass-independent, almost homogeneously scaling
distributions by a Taylor expansion in the mass $m$. The sm-expansion is a
generalization of this Taylor expansion, which yields this crucial
simplification of the renormalization of massive models also for the case that
one quantizes with the Wightman two-point function, which contains a
$\log(-(m^2(x^2-ix^0 0))$-term. We construct the general solution of the new
system of axioms (i.e. the usual axioms of causal perturbation theory completed
by the sm-expansion), and illustrate the method for a divergent diagram which
contains a divergent subdiagram.Comment: v2: some explanations added; 26 pages; version to appear in Ann.
  Henri Poincar
An extensive adiabatic invariant for the Klein-Gordon model in the
  thermodynamic limit

We construct an extensive adiabatic invariant for a Klein-Gordon chain in the
thermodynamic limit. In particular, given a fixed and sufficiently small value
of the coupling constant $a$, the evolution of the adiabatic invariant is
controlled up to times scaling as $\beta^{1/\sqrt{a}}$ for any large enough
value of the inverse temperature $\beta$. The time scale becomes a stretched
exponential if the coupling constant is allowed to vanish jointly with the
specific energy. The adiabatic invariance is exhibited by showing that the
variance along the dynamics, i.e. calculated with respect to time averages, is
much smaller than the corresponding variance over the whole phase space, i.e.
calculated with the Gibbs measure, for a set of initial data of large measure.
All the perturbative constructions and the subsequent estimates are consistent
with the extensive nature of the system.Comment: 60 pages. Minor corrections with respect to the first version. To
  appear in Annales Henri Poincar\'
Integrable QFT and Longo-Witten endomorphisms

Our previous constructions of Borchers triples are extended to massless
scattering with nontrivial left and right components. A massless Borchers
triple is constructed from a set of left-left, right-right and left-right
scattering functions. We find a correspondence between massless left-right
scattering S-matrices and massive block diagonal S-matrices. We point out a
simple class of S-matrices with examples.
  We study also the restriction of two-dimensional models to the lightray.
Several arguments for constructing strictly local two-dimensional nets are
presented and possible scenarios are discussed.Comment: 42 pages, 1 Tikz figure. The final version is available under Open
  Access. An erratum concerning Definition 3.4(4) of the right-mixed
  Yang-Baxter equation is available at
  http://dx.doi.org/10.1007/s00023-014-0337-1 . This arXiv version contains the
  corrected definitions and proposition
Characterization of the Quasi-Stationary State of an Impurity Driven by
  Monochromatic Light II - Microscopic Foundations

From quantum mechanical first principles only, we rigorously study the
time-evolution of a $N$-level atom (impurity) interacting with an external
monochromatic light source within an infinite system of free electrons at
thermal equilibrium (reservoir). In particular, we establish the relation
between the full dynamics of the compound system and the effective dynamics for
the $N$-level atom, which is studied in detail in [Bru-de Siqueira
Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370, 2012]. Together with
[Bru-de Siqueira Pedra-Westrich, Annales Henri Poincar\'e, 13(6):1305-1370,
2012] the present paper yields a purely microscopic theory of optical pumping
in laser physics. The model we consider is general enough to describe gauge
invariant atom-reservoir interactions
Zero modes of quantum graph Laplacians and an index theorem

We study zero modes of Laplacians on compact and non-compact metric graphs
with general self-adjoint vertex conditions. In the first part of the paper the
number of zero modes is expressed in terms of the trace of a unitary matrix
$\mathfrak{S}$ that encodes the vertex conditions imposed on functions in the
domain of the Laplacian. In the second part a Dirac operator is defined whose
square is related to the Laplacian. In order to accommodate Laplacians with
negative eigenvalues it is necessary to define the Dirac operator on a suitable
Kre\u{\i}n space. We demonstrate that an arbitrary, self-adjoint quantum graph
Laplacian admits a factorisation into momentum-like operators in a
Kre\u{\i}n-space setting. As a consequence, we establish an index theorem for
the associated Dirac operator and prove that the zero-mode contribution in the
trace formula for the Laplacian can be expressed in terms of the index of the
Dirac operator