The large-mass limit of interacting quantum gases in the continuum

TL;DR

This paper investigates the large-mass limit of quantum gases, showing they behave like classical particles, and provides explicit convergence rates using the Ginibre loop ensemble and cluster expansions.

Contribution

It extends the understanding of the continuum regime for quantum gases in the large-mass limit, including explicit convergence rates and analysis of infinite-volume behavior.

Findings

Quantum gases converge to classical interacting particles in the large-mass limit.

Explicit rates of convergence are obtained for finite-volume systems.

Infinite-volume behavior is analyzed using cluster expansions under certain conditions.

Abstract

We study the large-mass limit of interacting quantum (Bose or Fermi) gases in thermal equilibrium. We show that in the suitably-defined large-mass limit, the system gives rise to a gas of classical interacting particles. The corresponding question for bosons on a lattice was previously addressed by Fr\"{o}hlich, Knowles, Schlein, and the third author. In this work, we study the continuum regime which requires us to suitably tune the chemical potential. The starting point of our analysis is the Ginibre loop ensemble, which allows one to describe a system of interacting quantum gases in thermal equilibrium in terms of an ensemble of interacting Brownian paths. In a finite volume, our analysis is performed for stable and H\"{o}lder continuous interaction potentials and we are able to obtain explicit rates of convergence. When the interaction potential is nonnegative and satisfies suitable integrability conditions, we study the associated infinite-volume problem by means of cluster expansions.