pinecone/core-2020-05-10-deduplication huggingface dataset:
The effect of time-dependent coupling on non-equilibrium steady states

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
Dispersion relations in the noncommutative \phi^3 and Wess-Zumino model
  in the Yang-Feldman formalism

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
On confining potentials and essential self-adjointness for Schr\"odinger
  operators on bounded domains in R^n

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
Weyl laws for partially open quantum maps

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
Dynamical phase transition for a quantum particle source

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
A Gluing Construction Regarding Point Particles in General Relativity

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
The ground state and the long-time evolution in the CMC Einstein flow

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
A bijection between paths for the M(p,2p+1) minimal model Virasoro
  characters

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
Tiling groupoids and Bratteli diagrams

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
A time-dependent perturbative analysis for a quantum particle in a cloud
  chamber

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
Regularity results for the spherically symmetric Einstein-Vlasov system

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\'
Nonlocal potentials and complex angular momentum theory

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
Improved decay for solutions to the linear wave equation on a
  Schwarzschild black hole

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
Exponential renormalization

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
Classical and Quantum Behavior of the Integrated Density of States for a Randomly Perturbed Lattice

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
Wegner estimate for discrete alloy-type models

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
Global vs local Casimir effect

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
Localization Properties of the Chalker-Coddington Model

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
Chern-Simons Invariants of Torus Links

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
Ionization of Atoms by Intense Laser Pulses

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
On the construction of a geometric invariant measuring the deviation
  from Kerr data

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 a waveguide with frequently alternating boundary conditions:
  homogenized Neumann condition

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
Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

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
Symmetry breaking in quasi-1D Coulomb systems

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
Inverse scattering at fixed energy in de Sitter-Reissner-Nordstr\"om
  black holes

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