L2+ε -Esimates on Exponential Decay of Correlations in Equilibrium States of Classical Continuous Systems of Point Particles

Gennadiy Shchepanyuk

doi:10.13189/ujpa.2015.030103

Abstract

We present and prove L 2+e -estimates on exponential decay of correlations in equilibrium states of classical continuous systems of point particles interacting via an exponentially decaying pair potential of interaction, where e is arbitrary small and positive real number. The obtained estimates exhibit not only the explicit dependence on the distance between the areas of the equilibrium classical systems between which the correlations are estimated but also on the volume of these areas, which can be used in the future for the investigation of the corresponding non-equilibrium and dynamic systems.

Highlights

We provide and prove L2+ε-estimates on exponential decay of correlations in equilibrium states of classical continuous systems of point particles interacting via regular stable pair potential that exponentially decays with distance between particles
We obtain an explicit dependence of correlations on the distance between the regions of an equilibrium classical system of point particles and on their volumes, that, in the future, can be used for the investigation of the corresponding non-equilibrium and dynamic systems
The stability condition imposed on the pair potential of interaction ensures existence of the Gibbs state GzΛ,β(·) in the finite volume Λ ∈ L(Rd)

Summary

Introduction

We provide and prove L2+ε-estimates on exponential decay of correlations in equilibrium states of classical continuous systems of point particles interacting via regular stable pair potential that exponentially decays with distance between particles.

A Poisson Measure on the Configuration Space

Decay of Correlations