pinecone/core-2020-05-10-deduplication huggingface dataset:
Boundary triplets, tensor products and point contacts to reservoirs

We consider symmetric operators of the form $S := A\otimes I_{\mathfrak T} +
I_{\mathfrak H} \otimes T$ where $A$ is symmetric and $T = T^*$ is (in general)
unbounded. Such operators naturally arise in problems of simulating point
contacts to reservoirs. We construct a boundary triplet $\Pi_S$ for $S^*$
preserving the tensor structure. The corresponding $\gamma$-field and Weyl
function are expressed by means of the $\gamma$-field and Weyl function
corresponding to the boundary triplet $\Pi_A$ for $A^*$ and the spectral
measure of $T$. Applications to 1-D Schr\"odinger and Dirac operators are
given. A model of electron transport through a quantum dot assisted by cavity
photons is proposed. In this model the boundary operator is chosen to be the
well-known Jaynes-Cumming operator which is regarded as the Hamiltonian of the
quantum dot
On radial Schroedinger operators with a Coulomb potential

This paper presents a thorough analysis of 1-dimensional Schroedinger
operators whose potential is a linear combination of the Coulomb term 1/r and
the centrifugal term 1/r^2. We allow both coupling constants to be complex.
Using natural boundary conditions at 0, a two parameter holomorphic family of
closed operators is introduced. We call them the Whittaker operators, since in
the mathematical literature their eigenvalue equation is called the Whittaker
equation. Spectral and scattering theory for Whittaker operators is studied.
Whittaker operators appear in quantum mechanics as the radial part of the
Schroedinger operator with a Coulomb potential.Comment: 45 page
The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have
  Gaussian Maximizers

We determine the p->q norms of the Gaussian one-mode quantum-limited
attenuator and amplifier and prove that they are achieved by Gaussian states,
extending to noncommutative probability the seminal theorem "Gaussian kernels
have only Gaussian maximizers" (Lieb in Invent Math 102(1):179-208, 1990). The
quantum-limited attenuator and amplifier are the building blocks of quantum
Gaussian channels, which play a key role in quantum communication theory since
they model in the quantum regime the attenuation and the noise affecting any
electromagnetic signal. Our result is crucial to prove the longstanding
conjecture stating that Gaussian input states minimize the output entropy of
one-mode phase-covariant quantum Gaussian channels for fixed input entropy. Our
proof technique is based on a new noncommutative logarithmic Sobolev
inequality, and it can be used to determine the p->q norms of any quantum
semigroup.Comment: Annales Henri Poincar\'e (2018
Wick order, spreadability and exchangeability for monotone commutation
  relations

We exhibit a Hamel basis for the concrete $*$-algebra $\mathfrak{M}_o$
associated to monotone commutation relations realised on the monotone Fock
space, mainly composed by Wick ordered words of annihilators and creators. We
apply such a result to investigate spreadability and exchangeability of the
stochastic processes arising from such commutation relations. In particular, we
show that spreadability comes from a monoidal action implementing a dissipative
dynamics on the norm closure $C^*$-algebra $\mathfrak{M} =
\overline{\mathfrak{M}_o}$. Moreover, we determine the structure of spreadable
and exchangeable monotone stochastic processes using their correspondence with
sp\-reading invariant and symmetric monotone states, respectively.Comment: Ann. Henri Poincar\`e, to appea
Inverse scattering at fixed energy for radial magnetic Schr{\"o}dinger
  operators with obstacle in dimension two

We study an inverse scattering problem at fixed energy for radial magnetic
Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and
arbitrarily small radius. We assume that the magnetic potential A satisfies a
gauge condition and we consider the class C of smooth, radial and compactly
supported electric potentials and magnetic fields denoted by V and B
respectively. If (V, B) and (\tilde{V} , \tilde{B}) are two couples belonging
to C, we then show that if the corresponding phase shifts $\delta$\_l and
\tilde{$\delta$}\_l (i.e. the scattering data at fixed energy) coincide for all
l $\in$ L, where L $\subset$ N^$\star$ satisfies the M{\"u}ntz condition
\sum\_{l$\in$L} \frac{1}{l} = +$\infty$, then V (x) = \tilde{V}(x) and B(x) =
\tilde{B}(x) outside the obstacle B(0, r\_0). The proof use the Complex Angular
Momentum method and is close in spirit to the celebrated B{\"o}rg-Marchenko
uniqueness Theorem
Two-term spectral asymptotics for the Dirichlet pseudo-relativistic
  kinetic energy operator on a bounded domain

Continuing the series of works following Weyl's one-term asymptotic formula
for the counting function $N(\lambda)=\sum_{n=1}^\infty(\lambda_n{-}\lambda)_-$
of the eigenvalues of the Dirichlet Laplacian and the much later found two-term
expansion on domains with highly regular boundary by Ivrii and Melrose, we
prove a two-term asymptotic expansion of the $N$-th Ces\`aro mean of the
eigenvalues of $\sqrt{-\Delta + m^2} - m$ for $m>0$ with Dirichlet boundary
condition on a bounded domain $\Omega\subset\mathbb R^d$ for $d\geq 2$,
extending a result by Frank and Geisinger for the fractional Laplacian ($m=0$)
and improving upon the small-time asymptotics of the heat trace $Z(t) =
\sum_{n=1}^\infty e^{-t \lambda_n}$ by Ba\~nuelos et al. and Park and Song.Comment: Ann. Henri Poincar\'e (2018
Infinite volume limits in Euclidean quantum field theory via
  stereographic projection

We present a general infinite volume limit construction of probability
measures obeying the Glimm-Jaffe axioms of Euclidean quantum field theory in
arbitrary space-time dimension. In particular, we obtain measures that may be
interpreted as corresponding to scalar quantum fields with arbitrary bounded
continuous self-interaction. It remains however an open problem whether this
general construction contains non-Gaussian measures.Comment: New title. Final version, to appear in Annales Henri Poincar\'
Symmetry breaking in the periodic Thomas--Fermi--Dirac--von
  Weizs{\"a}cker model

We consider the Thomas--Fermi--Dirac--von~Weizs{\"a}cker model for a system
composed of infinitely many nuclei placed on a periodic lattice and electrons
with a periodic density. We prove that if the Dirac constant is small enough,
the electrons have the same periodicity as the nuclei. On the other hand if the
Dirac constant is large enough, the 2-periodic electronic minimizer is not
1-periodic, hence symmetry breaking occurs. We analyze in detail the behavior
of the electrons when the Dirac constant tends to infinity and show that the
electrons all concentrate around exactly one of the 8 nuclei of the unit cell
of size 2, which is the explanation of the breaking of symmetry. Zooming at
this point, the electronic density solves an effective nonlinear Schr\"odinger
equation in the whole space with nonlinearity $u^{7/3}-u^{4/3}$. Our results
rely on the analysis of this nonlinear equation, in particular on the
uniqueness and non-degeneracy of positive solutions
A Renormalizable SYK-type Tensor Field Theory

In this paper we introduce a simple field theoretic version of the
Carrozza-Tanasa-Klebanov-Tarnopolsky (CTKT) "uncolored" holographic tensor
model. It gives a more familiar interpretation to the previously abstract modes
of the SYK or CTKT models in terms of momenta. We choose for the tensor
propagator the usual Fermionic propagator of condensed matter, with a spherical
Fermi surface, but keep the CTKT interactions. Hence our field theory can also
be considered as an ordinary condensed matter model with a non-local and
non-rotational invariant interaction. Using a multiscale analysis we prove that
this field theory is just renormalizable to all orders of perturbation theory
in the ultraviolet regime.Comment: 24 pages, 2 figure
Necessary criterion for approximate recoverability

A tripartite state $\rho_{ABC}$ forms a Markov chain if there exists a
recovery map $\mathcal{R}_{B \to BC}$ acting only on the $B$-part that
perfectly reconstructs $\rho_{ABC}$ from $\rho_{AB}$. To achieve an approximate
reconstruction, it suffices that the conditional mutual information
$I(A:C|B)_{\rho}$ is small, as shown recently. Here we ask what conditions are
necessary for approximate state reconstruction. This is answered by a lower
bound on the relative entropy between $\rho_{ABC}$ and the recovered state
$\mathcal{R}_{B\to BC}(\rho_{AB})$. The bound consists of the conditional
mutual information and an entropic correction term that quantifies the
disturbance of the $B$-part by the recovery map.Comment: v2: 18 pages, final version published in Annales Henri Poincar\'
Universal recovery maps and approximate sufficiency of quantum relative
  entropy

The data processing inequality states that the quantum relative entropy
between two states $\rho$ and $\sigma$ can never increase by applying the same
quantum channel $\mathcal{N}$ to both states. This inequality can be
strengthened with a remainder term in the form of a distance between $\rho$ and
the closest recovered state $(\mathcal{R} \circ \mathcal{N})(\rho)$, where
$\mathcal{R}$ is a recovery map with the property that $\sigma = (\mathcal{R}
\circ \mathcal{N})(\sigma)$. We show the existence of an explicit recovery map
that is universal in the sense that it depends only on $\sigma$ and the quantum
channel $\mathcal{N}$ to be reversed. This result gives an alternate,
information-theoretic characterization of the conditions for approximate
quantum error correction.Comment: v3: 24 pages, 1 figure, final version published in Annales Henri
  Poincar\'
Quantum lattice gauge fields and groupoid C*-algebras

We present an operator-algebraic approach to the quantization and reduction
of lattice field theories. Our approach uses groupoid C*-algebras to describe
the observables and exploits Rieffel induction to implement the quantum gauge
symmetries. We introduce direct systems of Hilbert spaces and direct systems of
(observable) C*-algebras, and, dually, corresponding inverse systems of
configuration spaces and (pair) groupoids. The continuum and thermodynamic
limit of the theory can then be described by taking the corresponding limits,
thereby keeping the duality between the Hilbert space and observable C*-algebra
on the one hand, and the configuration space and the pair groupoid on the
other. Since all constructions are equivariant with respect to the gauge group,
the reduction procedure applies in the limit as well.Comment: 23 pages, 6 figure
Entanglement in non-local games and the hyperlinear profile of groups

We relate the amount of entanglement required to play linear-system non-local
games near-optimally to the hyperlinear profile of finitely-presented groups.
By calculating the hyperlinear profile of a certain group, we give an example
of a finite non-local game for which the amount of entanglement required to
play $\varepsilon$-optimally is at least $\Omega(1/\varepsilon^k)$, for some
$k>0$. Since this function approaches infinity as $\varepsilon$ approaches
zero, this provides a quantitative version of a theorem of the first author.Comment: 27 pages. v2: improved results based on a suggestion by N. Ozaw
The free boundary Schur process and applications I

We investigate the free boundary Schur process, a variant of the Schur
process introduced by Okounkov and Reshetikhin, where we allow the first and
the last partitions to be arbitrary (instead of empty in the original setting).
The pfaffian Schur process, previously studied by several authors, is recovered
when just one of the boundary partitions is left free. We compute the
correlation functions of the process in all generality via the free fermion
formalism, which we extend with the thorough treatment of "free boundary
states". For the case of one free boundary, our approach yields a new proof
that the process is pfaffian. For the case of two free boundaries, we find that
the process is not pfaffian, but a closely related process is. We also study
three different applications of the Schur process with one free boundary:
fluctuations of symmetrized last passage percolation models, limit shapes and
processes for symmetric plane partitions, and for plane overpartitions.Comment: 58 pages, 17 figures (v3: final version, with fewer pages than v2 to
  comply with journal requirements. In particular Theorems 2.2 and 2.5 are now
  stated under slightly more restrictive assumptions to simplify presentation.
  Added Remarks 2.11, 2.12, 5.14 and 6.9 about the transition from pfaffian to
  determinantal in the bulk.
Spectral Theory of Infinite Quantum Graphs

We investigate quantum graphs with infinitely many vertices and edges without
the common restriction on the geometry of the underlying metric graph that
there is a positive lower bound on the lengths of its edges. Our central result
is a close connection between spectral properties of a quantum graph and the
corresponding properties of a certain weighted discrete Laplacian on the
underlying discrete graph. Using this connection together with spectral theory
of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new
results on spectral properties of quantum graphs. Namely, we prove several
self-adjointness results including a Gaffney type theorem. We investigate the
problem of lower semiboundedness, prove several spectral estimates (bounds for
the bottom of spectra and essential spectra of quantum graphs, CLR-type
estimates) and study spectral types.Comment: Dedicated to the memory of M. Z. Solomyak (16.05.1931 - 31.07.2016
Relative entropy and entropy production for equilibrium states in pAQFT

We analyze the relative entropy of certain KMS states for scalar
self-interacting quantum field theories over Minkowski backgrounds that have
been recently constructed by Fredenhagen and Lindner in [FL14] in the framework
of perturbative algebraic quantum field theory. The definition we are using is
a generalization of the Araki relative entropy to the case of field theories.
In particular, we shall see that the analyzed relative entropy is positive in
the sense of perturbation theory, hence, even if the relative modular operator
is not at disposal in this context, the proposed extension is compatible with
perturbation theory. In the second part of the paper we analyze the adiabatic
limits of these states showing that also the density of relative entropy
obtained dividing the relative entropy by the spatial volume of the region
where interaction takes place is positive and finite. In the last part of the
paper we discuss the entropy production for states obtained by an ergodic mean
(time average) of perturbed KMS states evolved with the free evolution recently
constructed by the authors of the present paper. We show that their entropy
production vanishes even if return to equilibrium [Ro73, HKT74] does not hold.
This means that states constructed in this way are thermodynamically simple,
namely they are not so far from equilibrium states.Comment: 31 page
Tunneling for a class of Difference Operators: Complete Asymptotics

We analyze a general class of difference operators $H_\varepsilon =
T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon\mathbf{Z}^d)$, where
$V_\varepsilon$ is a multi-well potential and $\varepsilon$ is a small
parameter. We derive full asymptotic expansions of the prefactor of the
exponentially small eigenvalue splitting due to interactions between two
"wells" (minima) of the potential energy, i.e., for the discrete tunneling
effect. We treat both the case where there is a single minimal geodesic (with
respect to the natural Finsler metric induced by the leading symbol
$h_0(x,\xi)$ of $H_\varepsilon$) connecting the two minima and the case where
the minimal geodesics form an $\ell+1$ dimensional manifold, $\ell\geq 1$.
These results on the tunneling problem are as sharp as the classical results
for the Schr\"odinger operator in \cite{hesjo}. Technically, our approach is
pseudodifferential and we adapt techniques from \cite{hesjo2} and \cite{hepar}
to our discrete setting.Comment: 32 pages, 1 figur
Log-scale equidistribution of zeros of quantum ergodic eigensections

Under suitable hypotheses, a symplectic map can be quantized as a sequence of
unitary operators acting on the $N$th powers of a positive line bundle over a
K\"{a}hler manifold. We show that if the symplectic map has polynomial decay of
correlations, then there exists a density one subsequence of eigensections
whose masses and zeros become equidistributed in balls of logarithmically
shrinking radii of lengths $\lvert \log N \rvert^{-\gamma}$ for some constant
$\gamma > 0$ independent of $N$.Comment: The ergodicity assumption is relaxed from exponential to polynomial
  decay of correlation
Autonomous quantum machines and the finite sized Quasi-Ideal clock

Processes such as quantum computation, or the evolution of quantum cellular
automata are typically described by a unitary operation implemented by an
external observer. In particular, an interaction is generally turned on for a
precise amount of time, using a classical clock. A fully quantum mechanical
description of such a device would include a quantum description of the clock
whose state is generally disturbed because of the back-reaction on it. Such a
description is needed if we wish to consider finite sized autonomous quantum
machines requiring no external control. The extent of the back-reaction has
implications on how small the device can be, on the length of time the device
can run, and is required if we want to understand what a fully quantum
mechanical treatment of an observer would look like. Here, we consider the
implementation of a unitary by a finite sized device which we call the
"Quasi-Ideal clock", and show that the back-reaction on it can be made
exponentially small in the device's dimension with only a linear increase in
energy. As a result, an autonomous quantum machine need only be of modest size
and or energy. We are also able to solve a long-standing open problem by using
a finite sized quantum clock to approximate the continuous evolution of an
Idealised clock. The result has implications on the equivalence of different
paradigms of quantum thermodynamics, some which allow external control and some
which only allow autonomous thermal machines.Comment: Main text: 9 + 53 pages. V4: Close to the published version, J.
  Annales Henri Poincar\'e (2018) [Communicated by David P\'erez-Garc\'ia
On Wick polynomials of boson fields in locally covariant algebraic QFT

This work presents some results about Wick polynomials of a vector field
renormalization in locally covariant algebraic quantum field theory in curved
spacetime. General vector fields are pictured as sections of natural vector
bundles over globally hyperbolic spacetimes and quantized through the known
functorial machinery in terms of local $^*$-algebras. These quantized fields
may be defined on spacetimes with given classical background fields, also
sections of natural vector bundles, in addition to the Lorentzian metric. The
mass and the coupling constants are in particular viewed as background fields.
Wick powers of the quantized vector field are axiomatically defined imposing in
particular local covariance, scaling properties and smooth dependence on smooth
perturbation of the background fields. A general classification theorem is
established for finite renormalization terms (or counterterms) arising when
comparing different solutions satisfying the defining axioms of Wick powers.
The result is specialized to the case of general tensor fields. In particular,
the case of a vector Klein-Gordon field and the case of a scalar field
renormalized together with its derivatives are discussed as examples. In each
case, a more precise statement about the structure of the counterterms is
proved. The finite renormalization terms turn out to be finite-order
polynomials tensorially and locally constructed with the backgrounds fields and
their covariant derivatives whose coefficients are locally smooth functions of
polynomial scalar invariants constructed from the so-called marginal subset of
the background fields. The notion of local smooth dependence on polynomial
scalar invariants is made precise in the text.Comment: 63 pages, 2 figures, typos corrected, some comments added, accepted
  for publication in Annales Henri Poincar\'
Localised Wannier functions in metallic systems

The existence and construction of exponentially localised Wannier functions
for insulators is a well-studied problem. In comparison, the case of metallic
systems has been much less explored, even though localised Wannier functions
constitute an important and widely used tool for the numerical band
interpolation of metallic condensed matter systems. In this paper we prove
that, under generic conditions, $N$ energy bands of a metal can be exactly
represented by $N+1$ Wannier functions decaying faster than any polynomial. We
also show that, in general, the lack of a spectral gap does not allow for
exponential decay.Comment: 18 pages, 4 figure
Characterization of the frequency of extreme events by the Generalized
  Pareto Distribution

Based on recent results in extreme value theory, we use a new technique for
the statistical estimation of distribution tails. Specifically, we use the
Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for
peak-over-threshold values in the form of the Generalized Pareto Distribution
(GPD). Useful in finance, insurance, hydrology, we investigate here the
earthquake energy distribution described by the Gutenberg-Richter seismic
moment-frequency law and analyze shallow earthquakes (depth h < 70 km) in the
Harvard catalog over the period 1977-2000 in 18 seismic zones. The whole GPD is
found to approximate the tails of the seismic moment distributions quite well
above moment-magnitudes larger than mW=5.3 and no statistically significant
regional difference is found for subduction and transform seismic zones. We
confirm that the b-value is very different in mid-ocean ridges compared to
other zones (b=1.50=B10.09 versus b=1.00=B10.05 corresponding to a power law
exponent close to 1 versus 2/3) with a very high statistical confidence. We
propose a physical mechanism for this, contrasting slow healing ruptures in
mid-ocean ridges with fast healing ruptures in other zones. Deviations from the
GPD at the very end of the tail are detected in the sample containing
earthquakes from all major subduction zones (sample size of 4985 events). We
propose a new statistical test of significance of such deviations based on the
bootstrap method. The number of events deviating from the tails of GPD in the
studied data sets (15-20 at most) is not sufficient for determining the
functional form of those deviations. Thus, it is practically impossible to give
preference to one of the previously suggested parametric families describing
the ends of tails of seismic moment distributions.Comment: pdf document of 21 pages + 2 tables + 20 figures (ps format) + one
  file giving the regionalizatio