pinecone/core-2020-05-10-deduplication huggingface dataset:
A Theory of Intermittency Differentiation of 1D Infinitely Divisible
  Multiplicative Chaos Measures

A theory of intermittency differentiation is developed for a general class of
1D Infinitely Divisible Multiplicative Chaos measures. The intermittency
invariance of the underlying infinitely divisible field is established and
utilized to derive a Feynman-Kac equation for the distribution of the total
mass of the limit measure by considering a stochastic flow in intermittency.
The resulting equation prescribes the rule of intermittency differentiation for
a general functional of the total mass and determines the distribution of the
total mass and its dependence structure to the first order in intermittency. A
class of non-local functionals of the limit measure extending the total mass is
introduced and shown to be invariant under intermittency differentiation making
the computation of the full high temperature expansion of the total mass
distribution possible in principle. For application, positive integer moments
and covariance structure of the total mass are considered in detail.Comment: 38 page
Bulk-Edge correspondence for two-dimensional Floquet topological
  insulators

Floquet topological insulators describe independent electrons on a lattice
driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual
adiabatic approximation. In dimension two such systems are characterized by
integer-valued topological indices associated to the unitary propagator,
alternatively in the bulk or at the edge of a sample. In this paper we give new
definitions of the two indices, relying neither on translation invariance nor
on averaging, and show that they are equal. In particular weak disorder and
defects are intrinsically taken into account. Finally indices can be defined
when two driven sample are placed next to one another either in space or in
time, and then shown to be equal. The edge index is interpreted as a quantized
pumping occurring at the interface with an effective vacuum.Comment: 28 pages, 5 figures Minor changes, update and addition of some
  references To appear in Annales Henri Poincar\'
Compactness of the resolvent for the Witten Laplacian

In this paper we consider the Witten Laplacian on 0-forms and give sufficient
conditions under which the Witten Laplacian admits a compact resolvent. These
conditions are imposed on the potential itself, involving the control of high
order derivatives by lower ones, as well as the control of the positive
eigenvalues of the Hessian matrix. This compactness criterion for resolvent is
inspired by the one for the Fokker-Planck operator. Our method relies on the
nilpotent group techniques developed by Helffer-Nourrigat [Hypoellipticit\'e
maximale pour des op\'erateurs polyn\^omes de champs de vecteurs, 1985].Comment: 25page
Quantum compression relative to a set of measurements

In this work, we investigate the possibility of compressing a quantum system
to one of smaller dimension in a way that preserves the measurement statistics
of a given set of observables. In this process, we allow for an arbitrary
amount of classical side information. We find that the latter can be bounded,
which implies that the minimal compression dimension is stable in the sense
that it cannot be decreased by allowing for small errors. Various bounds on the
minimal compression dimension are proven and an SDP-based algorithm for its
computation is provided. The results are based on two independent approaches:
an operator algebraic method using a fixed point result by Arveson and an
algebro-geometric method that relies on irreducible polynomials and B\'ezout's
theorem. The latter approach allows lifting the results from the single copy
level to the case of multiple copies and from completely positive to merely
positive maps.Comment: 40 pages. Minor clarifications in Section 9.2 and Section 7.
Self-Adjointness of Dirac Operators with Infinite Mass Boundary
  Conditions in Sectors

This paper deals with the study of the two-dimensional Dirac operatorwith
infinite mass boundary condition in a sector. We investigate the question
ofself-adjointness depending on the aperture of the sector: when the sector is
convexit is self-adjoint on a usual Sobolev space whereas when the sector is
non-convexit has a family of self-adjoint extensions parametrized by a complex
number of theunit circle. As a byproduct of this analysis we are able to give
self-adjointnessresults on polygones. We also discuss the question of
distinguished self-adjointextensions and study basic spectral properties of the
operator in the sector
Large Strebel graphs and $(3,2)$ Liouville CFT

2D quantum gravity is the idea that a set of discretized surfaces (called
map, a graph on a surface), equipped with a graph measure, converges in the
large size limit (large number of faces) to a conformal field theory (CFT), and
in the simplest case to the simplest CFT known as pure gravity, also known as
the gravity dressed (3,2) minimal model. Here we consider the set of planar
Strebel graphs (planar trivalent metric graphs) with fixed perimeter faces,
with the measure product of Lebesgue measure of all edge lengths, submitted to
the perimeter constraints. We prove that expectation values of a large class of
observables indeed converge towards the CFT amplitudes of the (3,2) minimal
model.Comment: 35 pages, 6 figures, misprints corrected, presentation of appendix A
  modifie
Balance between quantum Markov semigroups

The concept of balance between two state preserving quantum Markov semigroups
on von Neumann algebras is introduced and studied as an extension of conditions
appearing in the theory of quantum detailed balance. This is partly motivated
by the theory of joinings. Balance is defined in terms of certain correlated
states (couplings), with entangled states as a specific case. Basic properties
of balance are derived and the connection to correspondences in the sense of
Connes is discussed. Some applications and possible applications, including to
non-equilibrium statistical mechanics, are briefly explored.Comment: v1: 40 pages. v2: Corrections and small additions made, 41 page
R\'enyi divergences as weighted non-commutative vector valued
  $L_p$-spaces

We show that Araki and Masuda's weighted non-commutative vector valued
$L_p$-spaces [Araki \& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)]
correspond to an algebraic generalization of the sandwiched R\'enyi divergences
with parameter $\alpha = \frac{p}{2}$. Using complex interpolation theory, we
prove various fundamental properties of these divergences in the setup of von
Neumann algebras, including a data-processing inequality and monotonicity in
$\alpha$. We thereby also give new proofs for the corresponding
finite-dimensional properties. We discuss the limiting cases $\alpha\to
\{\frac{1}{2},1,\infty\}$ leading to minus the logarithm of Uhlmann's fidelity,
Umegaki's relative entropy, and the max-relative entropy, respectively. As a
contribution that might be of independent interest, we derive a Riesz-Thorin
theorem for Araki-Masuda $L_p$-spaces and an Araki-Lieb-Thirring inequality for
states on von Neumann algebras.Comment: v2: 20 pages, published versio
Towards entanglement entropy with UV cutoff in conformal nets

We consider the entanglement entropy for a spacetime region and its spacelike
complement in the framework of algebraic quantum field theory. For a M\"obius
covariant local net satisfying a certain nuclearity property, we consider the
von Neumann entropy for type I factors between local algebras and introduce an
entropic quantity. Then we implement a cutoff on this quantity with respect to
the conformal Hamiltonian and show that it remains finite as the distance of
two intervals tends to zero. We compare our definition to others in the
literature.Comment: 23 page
The shape of the emerging condensate in effective models of condensation

We consider effective models of condensation where the condensation occurs as
time t goes to infinity. We provide natural conditions under which the build-up
of the condensate occurs on a spatial scale of 1/t and has the universal form
of a Gamma density. The exponential parameter of this density is determined
only by the equation and the total mass of the condensate, while the power law
parameter may in addition depend on the decay properties of the initial
condition near the condensation point. We apply our results to some examples,
including simple models of Bose-Einstein condensation
Derivation of an ornstein-uhlenbeck process for a massive particle in a
  rarified gas of particles

We consider the statistical motion of a convex rigid body in a gas of N
smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid
body is much bigger and heavier, it undergoes a lot of collisions leading to
small deflections. We prove that its velocity is described, in a suitable
limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on
Lanford's arguments [17] together with the pruning procedure from [3] to reach
diffusive times, much larger than the mean free time. Furthermore, we need to
introduce a modified dynamics to avoid pathological collisions of atoms with
the rigid body: these collisions, due to the geometry of the rigid body,
require developing a new type of trajectory analysis
On the Global Limiting Absorption Principle for Massless Dirac Operators

We prove a global limiting absorption principle on the entire real line for
free, massless Dirac operators $H_0 = \alpha \cdot (-i \nabla)$ for all space
dimensions $n \in \mathbb{N}$, $n \geq 2$. This is a new result for all
dimensions other than three, in particular, it applies to the two-dimensional
case which is known to be of some relevance in applications to graphene.
  We also prove an essential self-adjointness result for first-order
matrix-valued differential operators with Lipschitz coefficients.Comment: 22 page
Strong convergence of quantum random walks via semigroup decomposition

We give a simple and direct treatment of the strong convergence of quantum
random walks to quantum stochastic operator cocycles, via the semigroup
decomposition of such cocycles. Our approach also delivers convergence of the
pointwise product of quantum random walks to the quantum stochastic Trotter
product of the respective limit cocycles, thereby revealing the algebraic
structure of the limiting procedure. The repeated quantum interactions model is
shown to fit nicely into the convergence scheme described.Comment: 29 pages. To appear in the journal Annales Henri Poincare. Revisions
  made in v2; typos corrected in v3; final correction in v
Landauer's Principle for Trajectories of Repeated Interaction Systems

We analyze Landauer's principle for repeated interaction systems consisting
of a reference quantum system $\mathcal{S}$ in contact with an environment
$\mathcal{E}$ which is a chain of independent quantum probes. The system
$\mathcal{S}$ interacts with each probe sequentially, for a given duration, and
the Landauer principle relates the energy variation of $\mathcal{E}$ and the
decrease of entropy of $\mathcal{S}$ by the entropy production of the dynamical
process. We consider refinements of the Landauer bound at the level of the full
statistics (FS) associated to a two-time measurement protocol of, essentially,
the energy of $\mathcal{E}$. The emphasis is put on the adiabatic regime where
the environment, consisting of $T \gg 1$ probes, displays variations of order
$T^{-1}$ between the successive probes, and the measurements take place
initially and after $T$ interactions. We prove a large deviation principle and
a central limit theorem as $T \to \infty$ for the classical random variable
describing the entropy production of the process, with respect to the FS
measure. In a special case, related to a detailed balance condition, we obtain
an explicit limiting distribution of this random variable without rescaling. At
the technical level, we obtain a non-unitary adiabatic theorem generalizing
that of [Commun. Math. Phys. (2017) 349: 285] and analyze the spectrum of
complex deformations of families of irreducible completely positive
trace-preserving maps.Comment: 48 pages, 4 figures; fixed typos, made cosmetic changes, and added
  Lemma 5.5. To appear in Annales Henri Poincar\'
Existence of locally maximally entangled quantum states via geometric
  invariant theory

We study a question which has natural interpretations in both quantum
mechanics and in geometry. Let $V_1,..., V_n$ be complex vector spaces of
dimension $d_1,...,d_n$ and let $G= SL_{d_1} \times \dots \times SL_{d_n}$.
Geometrically, we ask given $(d_1,...,d_n)$, when is the geometric invariant
theory quotient $\mathbb{P}(V_1 \otimes \dots \otimes V_n)// G$ non-empty? This
is equivalent to the quantum mechanical question of whether the multipart
quantum system with Hilbert space $V_1\otimes \dots \otimes V_n$ has a locally
maximally entangled state, i.e. a state such that the density matrix for each
elementary subsystem is a multiple of the identity. We show that the answer to
this question is yes if and only if $R(d_1,...,d_n)\geqslant 0$ where \[
R(d_1,...,d_n) = \prod_i d_i +\sum_{k=1}^n (-1)^k \sum_{1\leq i_1<\dotsb
<i_k\leq n} (\gcd(d_{i_1},\dotsc ,d_{i_k}) )^{2}. \] We also provide a simple
recursive algorithm which determines the answer to the question, and we compute
the dimension of the resulting quotient in the non-empty cases.Comment: Improved the exposition and streamlined some proofs using results of
  Littelmann and Sato-Kimur
R\'enyi relative entropies and noncommutative $L_p$-spaces

We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy
to normal positive functionals on arbitrary von Neumann algebras, for the
values $\alpha>1$. For this, we use Kosaki's definition of noncommutative
$L_p$-spaces with respect to a state. Some properties of these extensions are
proved, in particular the limit values for $\alpha\to 1,\infty$ and data
processing inequality with respect to positive normal unital maps. This implies
that the Araki relative entropy satisfies DPI with respect to such maps,
extending the results of [A. M\"uller-Hermes and D. Reeb. Annales Henri
Poincar\'e 18, 1777-1788, 2017] to arbitrary von Neumann algebras. It is also
shown that equality in data processing inequality characterizes sufficiency
(reversibility) of quantum channels.Comment: 29 pages, minor changes and corrections. Comments welcom
Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

We establish the existence of $1$-parameter families of $\epsilon$-dependent
solutions to the Einstein-Euler equations with a positive cosmological constant
$\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq
1/3$, for the parameter values $0<\epsilon < \epsilon_0$. These solutions exist
globally to the future, converge as $\epsilon \searrow 0$ to solutions of the
cosmological Poison-Euler equations of Newtonian gravity, and are inhomogeneous
non-linear perturbations of FLRW fluid solutions.Comment: 58 pages. Agrees with published version. Note the title has been
  changed. Old title "Cosmological Newtonian limits on long time scales"; New
  title "Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
Algebraic quantum field theory on spacetimes with timelike boundary

We analyze quantum field theories on spacetimes $M$ with timelike boundary
from a model-independent perspective. We construct an adjunction which
describes a universal extension to the whole spacetime $M$ of theories defined
only on the interior $\mathrm{int}M$. The unit of this adjunction is a natural
isomorphism, which implies that our universal extension satisfies Kay's
F-locality property. Our main result is the following characterization theorem:
Every quantum field theory on $M$ that is additive from the interior (i.e.\
generated by observables localized in the interior) admits a presentation by a
quantum field theory on the interior $\mathrm{int}M$ and an ideal of its
universal extension that is trivial on the interior. We shall illustrate our
constructions by applying them to the free Klein-Gordon field.Comment: 27 pages, final version published in Annales Henri Poincar\'
The eleven dimensional supergravity equations on edge manifolds

We study the eleven dimensional supergravity equations which describe a low
energy approximation to string theories and are related to M-theory under the
AdS/CFT correspondence. These equations take the form of a non-linear
differential system, on $\mathbb{B}^7\times\mathbb{S}^4$ with the
characteristic degeneracy at the boundary of an edge system, associated to the
fibration with fiber $\mathbb{S}^4.$ We compute the indicial roots of the
linearized system from the Hodge decomposition of the 4-sphere following the
work of Kantor, then using the edge calculus and scattering theory we prove
that the moduli space of solutions, near the Freund--Rubin states, is
parametrized by three pairs of data on the bounding 6-sphere.Comment: 48 pages, 1 figure. To appear in Annales Henri Poincar
Product matrix processes for coupled multi-matrix models and their hard
  edge scaling limits

Product matrix processes are multi-level point processes formed by the
singular values of random matrix products. In this paper we study such
processes where the products of up to $m$ complex random matrices are no longer
independent, by introducing a coupling term and potentials for each product. We
show that such a process still forms a multi-level determinantal point
processes, and give formulae for the relevant correlation functions in terms of
the corresponding kernels.
  For a special choice of potential, leading to a Gaussian coupling between the
$m$th matrix and the product of all previous $m-1$ matrices, we derive a
contour integral representation for the correlation kernels suitable for an
asymptotic analysis of large matrix size $n$. Here, the correlations between
the first $m-1$ levels equal that of the product of $m-1$ independent matrices,
whereas all correlations with the $m$th level are modified. In the hard edge
scaling limit at the origin of the spectra of all products we find three
different asymptotic regimes. The first regime corresponding to weak coupling
agrees with the multi-level process for the product of $m$ independent complex
Gaussian matrices for all levels, including the $m$-th. This process was
introduced by one of the authors and can be understood as a multi-level
extension of the Meijer $G$-kernel introduced by Kuijlaars and Zhang. In the
second asymptotic regime at strong coupling the point process on level $m$
collapses onto level $m-1$, thus leading to the process of $m-1$ independent
matrices. Finally, in an intermediate regime where the coupling is proportional
to $n^{\frac12}$, we obtain a family of parameter dependent kernels,
interpolating between the limiting processes in the weak and strong coupling
regime. These findings generalise previous results of the authors and their
coworkers for $m=2$.Comment: 50 pages; v2 grant number added; v3 Remark and Proposition added,
  typo corrected, version to appear in AH
Variational characterization of the speed of reaction diffusion fronts
  for gradient dependent diffusion

We study the asymptotic speed of traveling fronts of the scalar reaction
diffusion for positive reaction terms and with a diffusion coefficient
depending nonlinearly on the concentration and on its gradient. We restrict our
study to diffusion coefficients of the form $D(u,u_x) = m u^{m-1} u_x^{m(p-2)}$
for which existence and convergence to traveling fronts has been established.
We formulate a variational principle for the asymptotic speed of the fronts.
Upper and lower bounds for the speed valid for any $m\ge0, p\ge 1$ are
constructed. When $m=1, p=2$ the problem reduces to the constant diffusion
problem and the bounds correspond to the classic Zeldovich Frank-Kamenetskii
lower bound and the Aronson-Weinberger upper bound respectively. In the special
case $m(p-1) = 1$ a local lower bound can be constructed which coincides with
the aforementioned upper bound. The speed in this case is completely determined
in agreement with recent results.Comment: 11 page
Contour methods for long-range Ising models: weakening nearest-neighbor
  interactions and adding decaying fields

We consider ferromagnetic long-range Ising models which display phase
transitions. They are long-range one-dimensional Ising ferromagnets, in which
the interaction is given by $J_{x,y} = J(|x-y|)\equiv
\frac{1}{|x-y|^{2-\alpha}}$ with $\alpha \in [0, 1)$, in particular, $J(1)=1$.
For this class of models one way in which one can prove the phase transition is
via a kind of Peierls contour argument, using the adaptation of the
Fr\"ohlich-Spencer contours for $\alpha \neq 0$, proposed by Cassandro,
Ferrari, Merola and Presutti. As proved by Fr\"ohlich and Spencer for
$\alpha=0$ and conjectured by Cassandro et al for the region they could treat,
$\alpha \in (0,\alpha_{+})$ for $\alpha_+=\log(3)/\log(2)-1$, although in the
literature dealing with contour methods for these models it is generally
assumed that $J(1)\gg1$, we can show that this condition can be removed in the
contour analysis. In addition, combining our theorem with a recent result of
Littin and Picco we prove the persistence of the contour proof of the phase
transition for any $\alpha \in [0,1)$. Moreover, we show that when we add a
magnetic field decaying to zero, given by $h_x= h_*\cdot(1+|x|)^{-\gamma}$ and
$\gamma >\max\{1-\alpha, 1-\alpha^* \}$ where $\alpha^*\approx 0.2714$, the
transition still persists.Comment: 13 page
Extended Riemannian Geometry I: Local Double Field Theory

We present an extended version of Riemannian geometry suitable for the
description of current formulations of double field theory (DFT). This
framework is based on graded manifolds and it yields extended notions of
symmetries, dynamical data and constraints. In special cases, we recover
general relativity with and without 1-, 2- and 3-form gauge potentials as well
as DFT. We believe that our extended Riemannian geometry helps to clarify the
role of various constructions in DFT. For example, it leads to a covariant form
of the strong section condition. Furthermore, it should provide a useful step
towards global and coordinate invariant descriptions of T- and U-duality
invariant field theories.Comment: v2: 50 pages, typos corrected, published versio
Orbital stability of solitary waves for generalized derivative nonlinear
  Schr\"odinger equations in the endpoint case

We consider the following generalized derivative nonlinear Schr\"odinger
equation \begin{equation*}
i\partial_tu+\partial^2_xu+i|u|^{2\sigma}\partial_xu=0,\ (t,x)\in\mathbb
R\times\mathbb R \end{equation*} when $\sigma\in(0,1)$. The equation has a
two-parameter family of solitary waves
$$u_{\omega,c}(t,x)=\Phi_{\omega,c}(x)e^{i\omega t+\frac{ic}2x-\frac
i{2\sigma+2}\int_0^x\Phi_{\omega,c}(y)^{2\sigma}dy},$$ with $(\omega,c)$
satisfying $\omega>c^2/4$, or $\omega=c^2/4$ and $c>0$. The stability theory in
the frequency region $\omega>c^2/4$ was studied previously. In this paper, we
prove the stability of the solitary wave solutions in the endpoint case
$\omega=c^2/4$ and $c>0$
Stabilization in the eye of a cyclone

We consider the systematic force on a heavy probe induced by interaction with
an overdamped diffusive medium where particles undergo a rotating force around
a fixed center. The stiffness matrix summarizes the stability of the probe
around that center, where the induced force vanishes. We prove that the
introduction of the rotational force in general enhances the stability of that
point (and may turn it from unstable to stable!), starting at second-order in
the nonequilibrium amplitude. When the driving is further enhanced the
stabilization occurs for a wide range of rotation profiles and the induced
stiffness converges to a universal expression proportional to the average
mechanical stiffness. The model thus provides a rigorous example of
stabilization of a fixed point due to contact with a nonequilibrium medium and
beyond linear order around equilibrium.Comment: 32 page