pinecone/core-2020-05-10-deduplication huggingface dataset:
On stable self-similar blow up for equivariant wave maps: The linearized
  problem

We consider co-rotational wave maps from (3+1) Minkowski space into the
three-sphere. This is an energy supercritical model which is known to exhibit
finite time blow up via self-similar solutions. The ground state self-similar
solution $f_0$ is known in closed form and based on numerics, it is supposed to
describe the generic blow up behavior of the system. In this paper we develop a
rigorous linear perturbation theory around $f_0$. This is an indispensable
prerequisite for the study of nonlinear stability of the self-similar blow up
which is conducted in a companion paper. In particular, we prove that $f_0$ is
linearly stable if it is mode stable. Furthermore, concerning the mode
stability problem, we prove new results that exclude the existence of unstable
eigenvalues with large imaginary parts and also, with real parts larger than
1/2. The remaining compact region is well-studied numerically and all available
results strongly suggest the nonexistence of unstable modes.Comment: 32 pages, 2 figures, acknowledgments adde
Bubble divergences: sorting out topology from cell structure

We conclude our analysis of bubble divergences in the flat spinfoam model. In
[arXiv:1008.1476] we showed that the divergence degree of an arbitrary
two-complex Gamma can be evaluated exactly by means of twisted cohomology.
Here, we specialize this result to the case where Gamma is the two-skeleton of
the cell decomposition of a pseudomanifold, and sharpen it with a careful
analysis of the cellular and topological structures involved. Moreover, we
explain in detail how this approach reproduces all the previous powercounting
results for the Boulatov-Ooguri (colored) tensor models, and sheds light on
algebraic-topological aspects of Gurau's 1/N expansion.Comment: 19 page
Massless interacting quantum fields in deSitter spacetime

We generalize key aspects of arXiv:1010.5367 (and also arXiv:1010.5327) to
the case of {\em massless} $\lambda \phi^{2n}$ quantum field theory on deSitter
spacetime. As in that paper, our key objective is to derive a suitable
"Mellin-Barnes-type" representation of deSitter correlation functions in a
deSitter-invariant state, which holds to arbitrary orders in perturbation
theory, and which incorporates renormalization. The representation is suitable
for the study of large distance/time properties of correlation functions. It is
arrived at via an analytic continuation from the corresponding objects on the
sphere, and, as in the massive case, relies on the use of graph-polynomials and
their properties, as well as other tools. However, the perturbation expansion
is organized somewhat differently in the massless case, due to the well-known
subtleties associated with the "zero-mode" of the quantum field. In particular,
the correlation functions do not possess a well-defined limit as the
self-coupling constant of the field goes to zero, reflecting the well-known
non-existence of a deSitter invariant state in the free massless scalar theory.
We establish that generic correlation functions cannot grow more than
polynomially in proper time for large time-like separations of the points. Our
results thus leave open the possibility of quantum induced IR-instabilities of
deSitter spacetime on very large time-scales.Comment: 40 pages, several figures, v2: added references, more discussion in
  app.C and in proof of thm.1, other minor change
Sums of magnetic eigenvalues are maximal on rotationally symmetric
  domains

The sum of the first n energy levels of the planar Laplacian with constant
magnetic field of given total flux is shown to be maximal among triangles for
the equilateral triangle, under normalization of the ratio (moment of
inertia)/(area)^3 on the domain. The result holds for both Dirichlet and
Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary
conditions too. The square similarly maximizes the eigenvalue sum among
parallelograms, and the disk maximizes among ellipses. More generally, a domain
with rotational symmetry will maximize the magnetic eigenvalue sum among all
linear images of that domain. These results are new even for the ground state
energy (n=1).Comment: 19 pages, 1 figur
A New Recursion Relation for the 6j-Symbol

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2)
representations. In the limit of large angular momenta, its asymptotics is
known to be described by the geometry of a tetrahedron with quantized lengths.
This article presents a new recursion formula for the square of the 6j-symbol.
In the asymptotic regime, the new recursion is shown to characterize the
closure of the relevant tetrahedron. Since the 6j-symbol is the basic building
block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we
also discuss how to generalize the method to derive more general recursion
relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured;
  Annales Henri Poincare (2011
Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads, and assume that
the total (continuous) system is at thermal equilibrium in the remote past. We
construct a non-equilibrium steady state (NESS) by adiabatically turning on an
electrical bias between the leads. The main mathematical challenge is to show
that certain adiabatic wave operators exist, and to identify their strong limit
when the adiabatic parameter tends to zero. Our NESS is different from, though
closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle
approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971
regarding the (non)equivalence between the partitioned and partition-free
approaches
Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry

In this paper, we show that massless Dirac waves in the Schwarzschild
geometry decay to zero at a rate $t^{-2\lambda}$, where $\lambda=1, 2,...$ is
the angular momentum. Our technique is to use Chandrasekhar's separation of
variables whereby the Dirac equations split into two sets of wave equations.
For the first set, we show that the wave decays as $t^{-2\lambda}$. For the
second set, in general, the solutions tend to some explicit profile at the rate
$t^{-2\lambda}$. The decay rate of solutions of Dirac equations is achieved by
showing that the coefficient of the explicit profile is exactly zero. The key
ingredients in the proof of the decay rate of solutions for the first set of
wave equations are an energy estimate used to show the absence of bound states
and zero energy resonance and the analysis of the spectral representation of
the solutions. The proof of asymptotic behavior for the solutions of the second
set of wave equations relies on careful analysis of the Green's functions for
time independent Schr\"odinger equations associated with these wave equations.Comment: 45 page
Self-gravitating Klein-Gordon fields in asymptotically Anti-de-Sitter
  spacetimes

We initiate the study of the spherically symmetric Einstein-Klein-Gordon
system in the presence of a negative cosmological constant, a model appearing
frequently in the context of high-energy physics. Due to the lack of global
hyperbolicity of the solutions, the natural formulation of dynamics is that of
an initial boundary value problem, with boundary conditions imposed at null
infinity. We prove a local well-posedness statement for this system, with the
time of existence of the solutions depending only on an invariant H^2-type norm
measuring the size of the Klein-Gordon field on the initial data. The proof
requires the introduction of a renormalized system of equations and relies
crucially on r-weighted estimates for the wave equation on asymptotically AdS
spacetimes. The results provide the basis for our companion paper establishing
the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this
system.Comment: 50 pages, v2: minor changes, to appear in Annales Henri Poincar\'
Second order semiclassics with self-generated magnetic fields

We consider the semiclassical asymptotics of the sum of negative eigenvalues
of the three-dimensional Pauli operator with an external potential and a
self-generated magnetic field $B$. We also add the field energy $\beta \int
B^2$ and we minimize over all magnetic fields. The parameter $\beta$
effectively determines the strength of the field. We consider the weak field
regime with $\beta h^{2}\ge {const}>0$, where $h$ is the semiclassical
parameter. For smooth potentials we prove that the semiclassical asymptotics of
the total energy is given by the non-magnetic Weyl term to leading order with
an error bound that is smaller by a factor $h^{1+\e}$, i.e. the subleading term
vanishes. However, for potentials with a Coulomb singularity the subleading
term does not vanish due to the non-semiclassical effect of the singularity.
Combined with a multiscale technique, this refined estimate is used in the
companion paper \cite{EFS3} to prove the second order Scott correction to the
ground state energy of large atoms and molecules.Comment: Small typos corrected on Sep 24, 201
Local and Global Analytic Solutions for a Class of Characteristic
  Problems of the Einstein Vacuum Equations in the "Double Null Foliation
  Gauge"

The main goal of this work consists in showing that the analytic solutions
for a class of characteristic problems for the Einstein vacuum equations have
an existence region larger than the one provided by the Cauchy-Kowalevski
theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove
this result we first describe a geometric way of writing the vacuum Einstein
equations for the characteristic problems we are considering, in a gauge
characterized by the introduction of a double null cone foliation of the
spacetime. Then we prove that the existence region for the analytic solutions
can be extended to a larger region which depends only on the validity of the
apriori estimates for the Weyl equations, associated to the "Bel-Robinson
norms". In particular if the initial data are sufficiently small we show that
the analytic solution is global. Before showing how to extend the existence
region we describe the same result in the case of the Burger equation, which,
even if much simpler, nevertheless requires analogous logical steps required
for the general proof. Due to length of this work, in this paper we mainly
concentrate on the definition of the gauge we use and on writing in a
"geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski
theorem is adapted to the characteristic problem for the Einstein equations and
we describe how the existence region can be extended in the case of the Burger
equation. Finally we describe the structure of the extension proof in the case
of the Einstein equations. The technical parts of this last result is the
content of a second paper.Comment: 68 page
Towards a construction of inclusive collision cross-sections in the
  massless Nelson model

The conventional approach to the infrared problem in perturbative quantum
electrodynamics relies on the concept of inclusive collision cross-sections. A
non-perturbative variant of this notion was introduced in algebraic quantum
field theory. Relying on these insights, we take first steps towards a
non-perturbative construction of inclusive collision cross-sections in the
massless Nelson model. We show that our proposal is consistent with the
standard scattering theory in the absence of the infrared problem and discuss
its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'
Torus knots and mirror symmetry

We propose a spectral curve describing torus knots and links in the B-model.
In particular, the application of the topological recursion to this curve
generates all their colored HOMFLY invariants. The curve is obtained by
exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved
conifold, and should be regarded as the mirror of the topological D-brane
associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we
derive the curve as the large N limit of the matrix model computing torus knot
invariants.Comment: 30 pages + appendix, 3 figure
A matrix model for the topological string II: The spectral curve and
  mirror geometry

In a previous paper, we presented a matrix model reproducing the topological
string partition function on an arbitrary given toric Calabi-Yau manifold.
Here, we study the spectral curve of our matrix model and thus derive, upon
imposing certain minimality assumptions on the spectral curve, the large volume
limit of the BKMP "remodeling the B-model" conjecture, the claim that
Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the
spectral invariants of its mirror curve.Comment: 1+37 page
Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity
Instanton Counting and Wall-Crossing for Orbifold Quivers

Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative {Mathematical expression} gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated with the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras
Averaged Pointwise Bounds for Deformations of Schrodinger Eigenfunctions

Let (M,g) be a n-dimensional compact Riemannian manifold. We consider the
magnetic deformations of semiclassical Schrodinger operators on M for a family
of magnetic potentials that depends smoothly on $k$ parameters $u$, for $k \geq
n$, and satisfies a generic admissibility condition. Define the deformed
Schrodinger eigenfunctions to be the $u$-parametrized semiclassical family of
functions on M that is equal to the unitary magnetic Schrodinger propagator
applied to the Schrodinger eigenfunctions. The main result of this article
states that the $L^2$ norms in $u$ of the deformed Schrodinger eigenfunctions
are bounded above and below by constants, uniformly on $M$ and in $\hbar$. In
particular, the result shows that this non-random perturbation "kills" the
blow-up of eigenfunctions. We give, as applications, an eigenfunction
restriction bound and a quantum ergodicity result.Comment: To appear in Annales Henri Poincar\'e. 23 pages. Background
  information on semiclassical wavefronts and eigenfunction concentration has
  been added. Some notational changes made as well. Further changes made were
  suggested by the refere
Existence of wave operators with time-dependent modifiers for the
  Sch\"odinger equations with long-range potentials on scattering manifolds

We construct time-dependent wave operators for Schr\"{o}dinger equations with
long-range potentials on a manifold $M$ with asymptotically conic structure. We
use the two space scattering theory formalism, and a reference operator on a
space of the form $\mathbb{R} \times \partial M$, where $\partial M$ is the
boundary of $M$ at infinity. We construct exact solutions to the
Hamilton-Jacobi equation on the reference system $\mathbb{R} \times \partial
M$, and prove the existence of the modified wave operators.Comment: 27 page
Future non-linear stability for reflection symmetric solutions of the
  Einstein-Vlasov system of Bianchi types II and VI$_0$

Using the methods developed for the Bianchi I case we have shown that a
boostrap argument is also suitable to treat the future non-linear stability for
reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types
II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution
with dust and the Ellis-MacCallum solution respectively. We have thus
generalized the results obtained by Rendall and Uggla in the case of locally
rotationally symmetric Bianchi II spacetimes to the reflection symmetric case.
However we needed to assume small data. For Bianchi VI$_0$ there is no
analogous previous result.Comment: 30 page
Repeated quantum non-demolition measurements: convergence and
  continuous-time limit

We analyze general enough models of repeated indirect measurements in which a
quantum system interacts repeatedly with randomly chosen probes on which Von
Neumann direct measurements are performed. We prove, under suitable hypotheses,
that the system state probability distribution converges after a large number
of repeated indirect measurements, in a way compatible with quantum wave
function collapse. Similarly a modified version of the system density matrix
converges. We show that the convergence is exponential with a rate given by
some relevant mean relative entropies. We also prove that, under appropriate
rescaling of the system and probe interactions, the state probability
distribution and the system density matrix are solutions of stochastic
differential equations modeling continuous-time quantum measurements. We
analyze the large time convergence of these continuous-time processes and prove
convergence.Comment: 44 pages, no figur
Ground States for a Stationary Mean-Field Model for a Nucleon

International audienceIn this paper we consider a variational problem related to a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants
Semi- and Non-relativistic Limit of the Dirac Dynamics with External
  Fields

We show how to approximate Dirac dynamics for electronic initial states by
semi- and non-relativistic dynamics. To leading order, these are generated by
the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is
related to $\sqrt{m^2 + \xi^2}$ and $\xi^2 / 2m$, respectively. Higher-order
corrections can in principle be computed to any order in the small parameter
v/c which is the ratio of typical speeds to the speed of light. Our results
imply the dynamics for electronic and positronic states decouple to any order
in v/c << 1.
  To decide whether to get semi- or non-relativistic effective dynamics, one
needs to choose a scaling for the kinetic momentum operator. Then the effective
dynamics are derived using space-adiabatic perturbation theory by Panati et. al
with the novel input of a magnetic pseudodifferential calculus adapted to
either the semi- or non-relativistic scaling.Comment: 42 page
Heat bounds and the blowtorch theorem

We study driven systems with possible population inversion and we give
optimal bounds on the relative occupations in terms of released heat. A precise
meaning to Landauer's blowtorch theorem (1975) is obtained stating that
nonequilibrium occupations are essentially modified by kinetic effects. Towards
very low temperatures we apply a Freidlin-Wentzel type analysis for continuous
time Markov jump processes. It leads to a definition of dominant states in
terms of both heat and escape rates.Comment: 11 pages; v2: minor changes, 1 reference adde
Effective dynamics of an electron coupled to an external potential in
  non-relativistic QED

In the framework of non-relativistic QED, we show that the renormalized mass
of the electron (after having taken into account radiative corrections) appears
as the kinematic mass in its response to an external potential force.
Specifically, we study the dynamics of an electron in a slowly varying external
potential and with slowly varying initial conditions and prove that, for a long
time, it is accurately described by an associated effective dynamics of a
Schr\"odinger electron in the same external potential and for the same initial
data, with a kinetic energy operator determined by the renormalized dispersion
law of the translation-invariant QED model.Comment: 22 pages, AMS Late
Diffusive limit for a quantum linear Boltzmann dynamics

In this article, I study the diffusive behavior for a quantum test particle
interacting with a dilute background gas. The model I begin with is a reduced
picture for the test particle dynamics given by a quantum linear Boltzmann
equation in which the gas particle scattering is assumed to occur through a
hard-sphere interaction. The state of the particle is represented by a density
matrix that evolves according to a translation-covariant Lindblad equation. The
main result is a proof that the particle's position distribution converges to a
Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version
  and corrected an error in the proof of Proposition 7.
A generalized topological recursion for arbitrary ramification

The Eynard-Orantin topological recursion relies on the geometry of a Riemann
surface S and two meromorphic functions x and y on S. To formulate the
recursion, one must assume that x has only simple ramification points. In this
paper we propose a generalized topological recursion that is valid for x with
arbitrary ramification. We justify our proposal by studying degenerations of
Riemann surfaces. We check in various examples that our generalized recursion
is compatible with invariance of the free energies under the transformation
(x,y) -> (y,x), where either x or y (or both) have higher order ramification,
and that it satisfies some of the most important properties of the original
recursion. Along the way, we show that invariance under (x,y) -> (y,x) is in
fact more subtle than expected; we show that there exists a number of counter
examples, already in the case of the original Eynard-Orantin recursion, that
deserve further study.Comment: 26 pages, 2 figure