596 research outputs found
Large deviations for cluster size distributions in a continuous classical many-body system
An interesting problem in statistical physics is the condensation of
classical particles in droplets or clusters when the pair-interaction is given
by a stable Lennard-Jones-type potential. We study two aspects of this problem.
We start by deriving a large deviations principle for the cluster size
distribution for any inverse temperature and particle
density in the thermodynamic limit. Here
is the close packing density. While in general the rate
function is an abstract object, our second main result is the
-convergence of the rate function toward an explicit limiting rate
function in the low-temperature dilute limit ,
such that for some
. The limiting rate function and its minimisers appeared in
recent work, where the temperature and the particle density were coupled with
the particle number. In the decoupled limit considered here, we prove that just
one cluster size is dominant, depending on the parameter . Under
additional assumptions on the potential, the -convergence along curves
can be strengthened to uniform bounds, valid in a low-temperature, low-density
rectangle.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1014 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Continuum percolation for Gibbsian point processes with attractive interactions
We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large β). The main results are bounds on percolation thresholds ρ ± (β) in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, canonical Gibbs measures with infinite volume, grand-canonical Gibbs measure
Fermionic and bosonic Laughlin state on thick cylinders
We investigate a many-body wave function for particles on a cylinder known as
Laughlin's function. It is the power of a Vandermonde determinant times a
Gaussian. Our main result is: in a many-particle limit, at fixed radius, all
correlation functions have a unique limit, and the limit state has a
non-trivial period in the axial direction. The result holds regardless how
large the radius is, for fermions as well as bosons. In addition, we explain
how the algebraic structure used in proofs relates to a ground state
perturbation series and to quasi-state decompositions, and we show that the
monomer-dimer function introduced in an earlier work is an exact, zero energy,
ground state of a suitable finite range Hamiltonian; this is interesting
because of formal analogies with some quantum spin chains.Comment: 49 page
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Mayer and virial series at low temperature
We analyze the Mayer pressure-activity and virial pressure-density series for a classical system of particles in continuous configuration space at low temperature. Particles interact via a finite range potential with an attractive tail. We propose physical interpretations of the Mayer and virial series' radius of convergence, valid independently of the question of phase transition: the Mayer radius corresponds to a fast increase from very small to finite density, and the virial radius corresponds to a cross-over from monatomic to polyatomic gas. Our results have consequences for the search of a low density, low temperature solid-gas phase transition, consistent with the Lee-Yang theorem for lattice gases and with the continuum Widom-Rowlinson mode
Continuum percolation for Gibbsian point processes with attractive interactions
We study the problem of continuum percolation in infinite volume Gibbs
measures for particles with an attractive pair potential, with a focus on low
temperatures (large ). The main results are bounds on percolation
thresholds in terms of the density rather than the chemical
potential or activity. In addition, we prove a variational formula for a large
deviations rate function for cluster size distributions. This formula
establishes a link with the Gibbs variational principle and a form of
equivalence of ensembles, and allows us to combine knowledge on finite volume,
canonical Gibbs measures with infinite volume, grand-canonical Gibbs measures.Comment: 22 pages. Corrected a statement on lattice gases, added referenc
Surface energy and boundary layers for a chain of atoms at low temperature
We analyze the surface energy and boundary layers for a chain of atoms at low
temperature for an interaction potential of Lennard-Jones type. The pressure
(stress) is assumed small but positive and bounded away from zero, while the
temperature goes to zero. Our main results are: (1) As at fixed positive pressure , the Gibbs measures and
for infinite chains and semi-infinite chains satisfy path large
deviations principles. The rate functions are bulk and surface energy
functionals and
. The minimizer of the surface functional
corresponds to zero temperature boundary layers. (2) The surface correction to
the Gibbs free energy converges to the zero temperature surface energy,
characterized with the help of the minimum of
. (3) The bulk Gibbs measure and Gibbs
free energy can be approximated by their Gaussian counterparts. (4) Bounds on
the decay of correlations are provided, some of them uniform in
A functional central limit theorem for a modulated network of infinite-server queues
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