Reduced Density Matrices of Quantum Gases. II. Cluster Property

Abstract

The reduced density matrices of quantum gases are studied by means of a Wiener integral representation described in a previous paper. They are shown to satisfy a cluster property in the form of an absolute integrability condition of the natural quantum analogues of the Ursell functions, considered as functions of the differences of their arguments. Use is made of the natural transposition to the quantum case of the algebraic formalism introduced by Ruelle in the classical case. By‐products are two results on the signs of the coefficients of the Mayer expansion, in the case of Maxwell‐Boltzmann and Fermi‐Dirac statistics, respectively.