pinecone/core-2020-05-10-deduplication huggingface dataset:
On the form factors of local operators in the Bazhanov-Stroganov and
  chiral Potts models

We consider general cyclic representations of the 6-vertex Yang-Baxter
algebra and analyze the associated quantum integrable systems, the
Bazhanov-Stroganov model and the corresponding chiral Potts model on finite
size lattices. We first determine the propagator operator in terms of the
chiral Potts transfer matrices and we compute the scalar product of separate
states (including the transfer matrix eigenstates) as a single determinant
formulae in the framework of Sklyanin's quantum separation of variables. Then,
we solve the quantum inverse problem and reconstruct the local operators in
terms of the separate variables. We also determine a basis of operators whose
form factors are characterized by a single determinant formulae. This implies
that the form factors of any local operator are expressed as finite sums of
determinants. Among these form factors written in determinant form are in
particular those which will reproduce the chiral Potts order parameters in the
thermodynamic limit.Comment: 45 page
Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic
  Space-Times

We give a complete framework for the Gupta-Bleuler quantization of the free
electromagnetic field on globally hyperbolic space-times. We describe
one-particle structures that give rise to states satisfying the microlocal
spectrum condition. The field algebras in the so-called Gupta-Bleuler
representations satisfy the time-slice axiom, and the corresponding vacuum
states satisfy the microlocal spectrum condition. We also give an explicit
construction of ground states on ultrastatic space-times. Unlike previous
constructions, our method does not require a spectral gap or the absence of
zero modes. The only requirement, the absence of zero-resonance states, is
shown to be stable under compact perturbations of topology and metric. Usual
deformation arguments based on the time-slice axiom then lead to a construction
of Gupta-Bleuler representations on a large class of globally hyperbolic
space-times. As usual, the field algebra is represented on an indefinite inner
product space, in which the physical states form a positive semi-definite
subspace. Gauge transformations are incorporated in such a way that the field
can be coupled perturbatively to a Dirac field. Our approach does not require
any topological restrictions on the underlying space-time.Comment: 28 pages, LaTeX, statement of Proposition 5.1 correcte
Resonances and Partial Delocalization on the Complete Graph

Random operators may acquire extended states formed from a multitude of
mutually resonating local quasi-modes. This mechanics is explored here in the
context of the random Schr\"odinger operator on the complete graph. The
operators exhibits local quasi modes mixed through a single channel. While most
of its spectrum consists of localized eigenfunctions, under appropriate
conditions it includes also bands of states which are delocalized in the
$\ell^1$-though not in $\ell^2$-sense, where the eigenvalues have the
statistics of \v{S}eba spectra. The analysis proceeds through some general
observations on the scaling limits of random functions in the Herglotz-Pick
class. The results are in agreement with a heuristic condition for the
emergence of resonant delocalization, which is stated in terms of the tunneling
amplitude among quasi-modes
Locally covariant quantum field theory with external sources

We provide a detailed analysis of the classical and quantized theory of a
multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime
metric and also to an external source term; thus the solutions form an affine
space. Following the formulation of affine field theories in terms of
presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171
(2014)], we determine the relative Cauchy evolution induced by metric as well
as source term perturbations and compute the automorphism group of natural
isomorphisms of the presymplectic vector space functor. Two pathological
features of this formulation are revealed: the automorphism group contains
elements that cannot be interpreted as global gauge transformations of the
theory; moreover, the presymplectic formulation does not respect a natural
requirement on composition of subsystems. We therefore propose a systematic
strategy to improve the original description of affine field theories at the
classical and quantized level, first passing to a Poisson algebra description
in the classical case. The idea is to consider state spaces on the classical
and quantum algebras suggested by the physics of the theory (in the classical
case, we use the affine solution space). The state spaces are not separating
for the algebras, indicating a redundancy in the description. Removing this
redundancy by a quotient, a functorial theory is obtained that is free of the
above mentioned pathologies. These techniques are applicable to general affine
field theories and Abelian gauge theories. The resulting quantized theory is
shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references
  added. v3: 47 pages; compatible with version to appear in Annales Henri
  Poincar
Static potentials on asymptotically flat manifolds

We consider the question whether a static potential on an asymptotically flat
3-manifold can have nonempty zero set which extends to the infinity. We prove
that this does not occur if the metric is asymptotically Schwarzschild with
nonzero mass. If the asymptotic assumption is relaxed to the usual assumption
under which the total mass is defined, we prove that the static potential is
unique up to scaling unless the manifold is flat. We also provide some
discussion concerning the rigidity of complete asymptotically flat 3-manifolds
without boundary that admit a static potential.Comment: introduction revised; an outline of a space-time approach adde
Deformations of Charged Axially Symmetric Initial Data and the
  Mass-Angular Momentum-Charge Inequality

We show how to reduce the general formulation of the mass-angular
momentum-charge inequality, for axisymmetric initial data of the
Einstein-Maxwell equations, to the known maximal case whenever a geometrically
motivated system of equations admits a solution. It is also shown that the same
reduction argument applies to the basic inequality yielding a lower bound for
the area of black holes in terms of mass, angular momentum, and charge. This
extends previous work by the authors [4] (arXiv:1401.3384), in which the role
of charge was omitted. Lastly, we improve upon the hypotheses required for the
mass-angular momentum-charge inequality in the maximal case.Comment: 34 pages; final version. This article builds on previous work of the
  authors (arXiv:1401.3384) by including the electromagnetic fiel
On Self-Adjoint Extensions and Symmetries in Quantum Mechanics

Given a unitary representation of a Lie group G on a Hilbert space H , we develop the theory of G-invariant self-adjoint extensions of symmetric operators using both von Neumann's theorem and the theory of quadratic forms. We also analyze the relation between the reduction theory of the unitary representation and the reduction of the G-invariant unbounded operator. We also prove a G-invariant version of the representation theorem for closed and semi-bounded quadratic forms. The previous results are applied to the study of G-invariant self-adjoint extensions of the Laplace&-Beltrami operator on a smooth Riemannian manifold with boundary on which the group G acts. These extensions are labeled by admissible unitaries U acting on the L 2-space at the boundary and having spectral gap at &#8722;1. It is shown that if the unitary representation V of the symmetry group G is traceable, then the self-adjoint extension of the Laplace&-Beltrami operator determined by U is G-invariant if U and V commute at the boundary. Various significant examples are discussed at the end.A. Ibort and J. M. Pérez-Pardo are partly supported by the project MTM2010-21186-C02-02 of the spanish Ministerio de Ciencia e Innovación and QUITEMAD programme P2009
ESP-1594. F. Lledó was partially supported by projects DGI MICIIN MTM2012-36372-C03-01 and Severo Ochoa SEV-2011-0087 of the spanish Ministry of Economy and Competition.
J. M. Pérez-Pardo was also partially supported in 2011 and 2012 by mobility grants of the “Universidad Carlos III de Madrid”
Natural extensions of electroweak geometry and Higgs interactions

We explore the possibility that the Higgs boson of the standard model be
actually a member of a larger family, by showing that a more elaborate internal
structure naturally arises from geometrical arguments, in the context of a
partly original handling of gauge fields which was put forward in previous
papers. A possible mechanism yielding the usual Higgs potential is proposed.
New types of point interactions, arising in particular from two-spinor index
contractions, are shown to be allowed.Comment: Corrected typos and added journal info, Annales Henri Poincar\'e
  (2014). Springer link:
  http://link.springer.com/article/10.1007/s00023-014-0383-
Exact results for a toy model exhibiting dynamic criticality

In this article we discuss an exactly solvable, one-dimensional, periodic toy
charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103},
46002 (2013)]. In particular, driving the system with a uniform force, we show
that the depinning threshold configuration is an explicit function of the
underlying disorder, as is the evolution from the negative threshold to the
positive threshold, the latter admitting a description in terms of record
sequences. This evolution is described by an avalanche algorithm, which
identifies a sequence of static configurations that are stable at successively
stronger forcing, and is useful both for analysis and simulation. We focus in
particular on the behavior of the polarization $P$, which is related to the
cumulative avalanche size, as a function of the threshold force minus the
current force $(F_{\mathrm{th}} - F)$, as this has been the focus of several
prior numerical and analytical studies of CDW systems. The results presented
are rigorous, with exceptions explicitly indicated, and show that the depinning
transition in this model is indeed a dynamic critical phenomenon
Characterization of bulk states in one-edge quantum Hall systems

We study magnetic quantum Hall systems in a half-plane with Dirichlet boundary conditions along the edge. Much work has been done on the analysis of the currents associated with states whose energy is located between Landau levels. These edge states are localized near the boundary and they carry a non-zero current. In this article, we study the behavior of states with energy close to a Landau level that are referred to as bulk states in the physics literature. The magnetic Schrödinger operator is invariant with respect to translations in the direction of the edge and is a direct integral of operators indexed by a real wave number. We analyse the fiber operators and prove new asymptotics on the band functions and their first derivative as the wave number goes to infinity. We apply these results to prove that the current carried by a bulk state is small compared to the current carried by an edge state. We also prove that the bulk states are exponentially small near the edge
Instability of pre-existing resonances under a small constant electric
  field

Two simple model operators are considered which have pre-existing resonances.
A potential corresponding to a small electric field, $f$, is then introduced
and the resonances of the resulting operator are considered as $f\to0$. It is
shown that these resonances are not continuous in this limit. It is conjectured
that a similar behavior will appear in more complicated models of atoms and
molecules. Numerical results are presented.Comment: 54 pages, 11 figures. No changes w.r.t. preprint version of
  03/29/2014, except publisher information added. The final publication is
  available at link.springer.co
Rational differential systems, loop equations, and application to the
  q-th reductions of KP

To any solution of a linear system of differential equations, we associate a
kernel, correlators satisfying a set of loop equations, and in presence of
isomonodromic parameters, a Tau function. We then study their semiclassical
expansion (WKB type expansion in powers of the weight hbar per derivative) of
these quantities. When this expansion is of topological type (TT), the
coefficients of expansions are computed by the topological recursion with
initial data given by the semiclassical spectral curve of the linear system.
This provides an efficient algorithm to compute them at least when the
semiclassical spectral curve is of genus 0. TT is a non trivial property, and
it is an open problem to find a criterion which guarantees it is satisfied. We
prove TT and illustrate our construction for the linear systems associated to
the q-th reductions of KP - which contain the (p,q) models as a specialization.Comment: 49 page
Spectral flows associated to flux tubes

When a flux quantum is pushed through a gapped two-dimensional tight-binding
operator, there is an associated spectral flow through the gap which is shown
to be equal to the index of a Fredholm operator encoding the topology of the
Fermi projection. This is a natural mathematical formulation of Laughlin's
Gedankenexperiment. It is used to provide yet another proof of the bulk-edge
correspondence. Furthermore, when applied to systems with time reversal
symmetry, the spectral flow has a characteristic $Z_2$ signature, while for
particle-hole symmetric systems it leads to a criterion for the existence of
zero energy modes attached to half-flux tubes. Combined with other results,
this allows to explain all strong invariants of two-dimensional topological
insulators in terms of a single Fredholm operator.Comment: final version, to appear in Ann. H. Poincar
Boundary quantum Knizhnik-Zamolodchikov equations and fusion

In this paper we extend our previous results concerning Jackson integral
solutions of the boundary quantum Knizhnik-Zamolodchikov equations with
diagonal K-operators to higher-spin representations of quantum affine
$\mathfrak{sl}_2$. First we give a systematic exposition of known results on
$R$-operators acting in the tensor product of evaluation representations in
Verma modules over quantum $\mathfrak{sl}_2$. We develop the corresponding
fusion of $K$-operators, which we use to construct diagonal $K$-operators in
these representations. We construct Jackson integral solutions of the
associated boundary quantum Knizhnik-Zamolodchikov equations and explain how in
the finite-dimensional case they can be obtained from our previous results by
the fusion procedure.Comment: 36 pages; some small additions and corrections concerning
  mero-uniform convergence (Defn. 6.1) and rectified some notation issues for
  the function \mathcal{Y} (p21 and onwards). appears in Annales Henri
  Poincar\'e, 201
Semi-classical analysis of non self-adjoint transfer matrices in
  statistical mechanics. I

We propose a way to study one-dimensional statistical mechanics models with
complex-valued action using transfer operators. The argument consists of two
steps. First, the contour of integration is deformed so that the associated
transfer operator is a perturbation of a normal one. Then the transfer operator
is studied using methods of semi-classical analysis.
  In this paper we concentrate on the second step, the main technical result
being a semi-classical estimate for powers of an integral operator which is
approximately normal.Comment: 28 pp, improved the presentatio
Dynamical locality of the free Maxwell field

We consider the non-interacting source-free Maxwell field, described both in
terms of the vector potential and the field strength. Starting from the
classical field theory on contractible globally hyperbolic spacetimes, we
extend the classical field theory to general globally hyperbolic spacetimes in
two ways to obtain a "universal" theory and a "reduced" theory. The quantum
field theory in terms of the unital $*$-algebra of the smeared quantum field is
then obtained by an application of a suitable quantisation functor. We show
that the universal theories fail local covariance and dynamical locality owing
to the possibility of having non-trivial radicals in the classical and
non-trivial centres in the quantum case. The reduced theories are both locally
covariant and dynamically local. These models provide new examples relevant to
the discussion of how theories should be formulated so as to describe the same
physics in all spacetimes.Comment: 27pp v3: Some comments added; minor corrections and typos fixe
Mixing for some non-uniformly hyperbolic systems

Author's manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-015-0399-8First available online: 14 February 2015In this work, we present an abstract framework that allows to obtain mixing (and in some cases sharp mixing) rates for a reasonable large class of invertible systems preserving an infinite measure. The examples explicitly considered are the invertible analogue of both Markov and non-Markov unit interval maps. For these examples, in addition to optimal results on mixing and rates of mixing in the infinite case, we obtain results on the decay of correlation in the finite case of invertible non-Markov maps, which, to our knowledge, were not previously addressed. The proposed method consists of a combination of the framework of operator renewal theory, as introduced in the context of dynamical systems by Sarig (Invent Math 150:629–653, 2002), with the framework of function spaces of distributions developed in the recent years along the lines of Blank et al. (Nonlinearity 15:1905–1973, 2001).European Research Council (ERC
Construction of real-valued localized composite Wannier functions for
  insulators

We consider a real periodic Schr\"odinger operator and a physically relevant
family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the
spectrum, and we investigate the localization properties of the corresponding
composite Wannier functions. To this aim, we show that in dimension $d \leq 3$
there exists a global frame consisting of smooth quasi-Bloch functions which
are both periodic and time-reversal symmetric. Aiming to applications in
computational physics, we provide a constructive algorithm to obtain such a
Bloch frame. The construction yields the existence of a basis of composite
Wannier functions which are real-valued and almost-exponentially localized.
  The proof of the main result exploits only the fundamental symmetries of the
projector on the relevant bands, allowing applications, beyond the model
specified above, to a broad range of gapped periodic quantum systems with a
time-reversal symmetry of bosonic type.Comment: 40 pages, 3 figures. Minor corrections implemented, some references
  added. To appear in Annales Henri Poicar\'
On the Existence of a Maximal Cauchy Development for the Einstein
  Equations - a Dezornification

In 1969, Choquet-Bruhat and Geroch established the existence of a unique
maximal globally hyperbolic Cauchy development of given initial data for the
Einstein equations. Their proof, however, has the unsatisfactory feature that
it relies crucially on the axiom of choice in the form of Zorn's lemma. In this
paper we present a proof that avoids the use of Zorn's lemma. In particular, we
provide an explicit construction of this maximal globally hyperbolic
development.Comment: 25 pages, 6 figures, v2 small changes and minor correction, v3
  version accepted for publicatio
On the K-theoretic classification of topological phases of matter

We present a rigorous and fully consistent $K$-theoretic framework for
studying gapped topological phases of free fermions such as topological
insulators. It utilises and profits from powerful techniques in operator
$K$-theory. From the point of view of symmetries, especially those of time
reversal, charge conjugation, and magnetic translations, operator $K$-theory is
more general and natural than the commutative topological theory. Our approach
is model-independent, and only the symmetry data of the dynamics, which may
include information about disorder, is required. This data is completely
encoded in a suitable $C^*$-superalgebra. From a representation-theoretic point
of view, symmetry-compatible gapped phases are classified by the
super-representation group of this symmetry algebra. Contrary to existing
literature, we do not use $K$-theory to classify phases in an absolute sense,
but only relative to some arbitrary reference. $K$-theory groups are better
thought of as groups of obstructions between homotopy classes of gapped phases.
Besides rectifying various inconsistencies in the existing literature on
$K$-theory classification schemes, our treatment has conceptual simplicity in
its treatment of all symmetries equally. The Periodic Table of Kitaev is
exhibited as a special case within our framework, and we prove that the
phenomena of periodicity and dimension shifts are robust against disorder and
magnetic fields.Comment: 41 pages, revised version with a new abstract, introductory sections
  and critique of the literatur
Time flat surfaces and the monotonicity of the spacetime Hawking mass II

In this sequel paper we give a shorter, second proof of the monotonicity of
the Hawking mass for time flat surfaces under spacelike uniformly area
expanding flows in spacetimes that satisfy the dominant energy condition. We
also include a third proof which builds on a known formula and describe a class
of sufficient conditions of divergence type for the monotonicity of the Hawking
mass. These flows of surfaces may have connections to the problem in general
relativity of bounding the total mass of a spacetime from below by the
quasi-local mass of spacelike 2-surfaces in the spacetime.Comment: 19 pages, 1 figur
Matrix models from operators and topological strings

We propose a new family of matrix models whose 1/N expansion captures the
all-genus topological string on toric Calabi-Yau threefolds. These matrix
models are constructed from the trace class operators appearing in the
quantization of the corresponding mirror curves. The fact that they provide a
non-perturbative realization of the (standard) topological string follows from
a recent conjecture connecting the spectral properties of these operators, to
the enumerative invariants of the underlying Calabi-Yau threefolds. We study in
detail the resulting matrix models for some simple geometries, like local P^2
and local F_2, and we verify that their weak 't Hooft coupling expansion
reproduces the topological string free energies near the conifold singularity.
These matrix models are formally similar to those appearing in the Fermi-gas
formulation of Chern-Simons-matter theories, and their 1/N expansion receives
non-perturbative corrections determined by the Nekrasov-Shatashvili limit of
the refined topological string.Comment: 30 pages, 6 figures; v2 : typos corrected, comments adde
The global anomaly of the self-dual field in general backgrounds

We prove a formula for the global gravitational anomaly of the self-dual
field theory in the presence of background gauge fields, assuming the results
of arXiv:1110.4639. Along the way, we also clarify various points about the
self-dual field theory. In particular, we give a general definition of the
theta characteristic entering its partition function and settle the issue of
its possible metric dependence. We treat the cohomological version of type IIB
supergravity as an example of the formalism: a mixed gauge-gravitational global
anomaly, occurring when the B-field and Ramond-Ramond 2-form gauge fields have
non-trivial Wilson lines, cancels provided a certain cobordism group vanishes.Comment: 38 pages. v3: Corrections in the discussion of the global anomaly
  cancellation in type IIB sugra. Typos correcte