193 research outputs found
The No-Binding Regime of the Pauli-Fierz Model
The Pauli-Fierz model in nonrelativistic quantum electrodynamics
is considered. The external potential is sufficiently shallow and the
dipole approximation is assumed. It is proven that there exist constants
such that has no ground state for
, which complements an earlier result stating that there is
a ground state for . We develop a suitable extension of
the Birman-Schwinger argument. Moreover for any given examples of
potentials are provided such that .Comment: 18 pages and 1 figur
Ground States in the Spin Boson Model
We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory
Mean-Field- and Classical Limit of Many-Body Schr\"odinger Dynamics for Bosons
We present a new proof of the convergence of the N-particle Schroedinger
dynamics for bosons towards the dynamics generated by the Hartree equation in
the mean-field limit. For a restricted class of two-body interactions, we
obtain convergence estimates uniform in the Planck constant , up to an
exponentially small remainder. For h=0, the classical dynamics in the
mean-field limit is given by the Vlasov equation.Comment: Latex 2e, 18 page
Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the dynamical large deviations for a particle system in which
particles may have different velocities. We assume that we have two infinite
reservoirs of particles at the boundary: this is the so-called boundary driven
process. The dynamics we considered consists of a weakly asymmetric simple
exclusion process with collision among particles having different velocities
Approach to ground state and time-independent photon bound for massless spin-boson models
It is widely believed that an atom interacting with the electromagnetic field
(with total initial energy well-below the ionization threshold) relaxes to its
ground state while its excess energy is emitted as radiation. Hence, for large
times, the state of the atom+field system should consist of the atom in its
ground state, and a few free photons that travel off to spatial infinity.
Mathematically, this picture is captured by the notion of asymptotic
completeness. Despite some recent progress on the spectral theory of such
systems, a proof of relaxation to the ground state and asymptotic completeness
was/is still missing, except in some special cases (massive photons, small
perturbations of harmonic potentials). In this paper, we partially fill this
gap by proving relaxation to an invariant state in the case where the atom is
modelled by a finite-level system. If the coupling to the field is sufficiently
infrared-regular so that the coupled system admits a ground state, then this
invariant state necessarily corresponds to the ground state. Assuming slightly
more infrared regularity, we show that the number of emitted photons remains
bounded in time. We hope that these results bring a proof of asymptotic
completeness within reach.Comment: 45 pages, published in Annales Henri Poincare. This archived version
differs from the journal version because we corrected an inconsequential
mistake in Section 3.5.1: to do this, a new paragraph was added after Lemma
3.
Dobrushin states in the \phi^4_1 model
We consider the van der Waals free energy functional in a bounded interval
with inhomogeneous Dirichlet boundary conditions imposing the two stable phases
at the endpoints. We compute the asymptotic free energy cost, as the length of
the interval diverges, of shifting the interface from the midpoint. We then
discuss the effect of thermal fluctuations by analyzing the \phi^4_1-measure
with Dobrushin boundary conditions. In particular, we obtain a nontrivial limit
in a suitable scaling in which the length of the interval diverges and the
temperature vanishes. The limiting state is not translation invariant and
describes a localized interface. This result can be seen as the probabilistic
counterpart of the variational convergence of the associated excess free
energy.Comment: 34 page
Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits
We present and discuss the derivation of a nonlinear non-local
integro-differential equation for the macroscopic time evolution of the
conserved order parameter of a binary alloy undergoing phase segregation. Our
model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics,
i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to
the Gibbs measure for a Hamiltonian which includes both short range (local) and
long range (nonlocal) interactions. A rigorous derivation is presented in the
case in which there is no local interaction. In a subsequent paper (part II),
we discuss the phase segregation phenomena in the model. In particular we argue
that the phase boundary evolutions, arising as sharp interface limits of the
family of equations derived in this paper, are the same as the ones obtained
from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page
Stokes-vector evolution in a weakly anisotropic inhomogeneous medium
Equation for evolution of the four-component Stokes vector in weakly
anisotropic and smoothly inhomogeneous media is derived on the basis of
quasi-isotropic approximation of the geometrical optics method, which provides
consequent asymptotic solution of Maxwell equations. Our equation generalizes
previous results, obtained for the normal propagation of electromagnetic waves
in stratified media. It is valid for curvilinear rays with torsion and is
capable to describe normal modes conversion in the inhomogeneous media.
Remarkably, evolution of the Stokes vector is described by the
Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the
equation for the three-component Stokes vector resembles the Landau-Lifshitz
equation for spin precession in ferromegnetic systems. General theory is
applied for analysis of polarization evolution in a magnetized plasma. We also
emphasize fundamental features of the non-Abelian polarization evolution in
anisotropic inhomogeneous media and illustrate them by simple examples.Comment: 16 pages, 3 figures, to appear in J. Opt. Soc. Am.
Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
For the symmetric simple exclusion process on an infinite line, we calculate
exactly the fluctuations of the integrated current during time
through the origin when, in the initial condition, the sites are occupied with
density on the negative axis and with density on the positive
axis. All the cumulants of grow like . In the range where , the decay of the distribution of is
non-Gaussian. Our results are obtained using the Bethe ansatz and several
identities recently derived by Tracy and Widom for exclusion processes on the
infinite line.Comment: 2 figure
Delay Equations and Radiation Damping
Starting from delay equations that model field retardation effects, we study
the origin of runaway modes that appear in the solutions of the classical
equations of motion involving the radiation reaction force. When retardation
effects are small, we argue that the physically significant solutions belong to
the so-called slow manifold of the system and we identify this invariant
manifold with the attractor in the state space of the delay equation. We
demonstrate via an example that when retardation effects are no longer small,
the motion could exhibit bifurcation phenomena that are not contained in the
local equations of motion.Comment: 15 pages, 1 figure, a paragraph added on page 5; 3 references adde
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