On Non Ergodic Property of Bose Gas with Weak Pair Interaction

TL;DR

This paper demonstrates that Bose gases with weak pair interactions are non-ergodic systems, highlighting the importance of boundary behavior in reaching thermal equilibrium and developing a renormalization theory for divergence analysis.

Contribution

It introduces a novel proof of non-ergodicity in Bose gases with weak interactions and develops a renormalization framework for divergence analysis in nonequilibrium diagrams.

Findings

Bose gas with weak pair interaction is non-ergodic.

Divergences in nonequilibrium diagrams are analogous to kinetic equation divergences.

Boundary effects are crucial for thermalization in such systems.

Abstract

In this paper we prove that Bose gas with weak pair interaction is non ergodic system. In order to prove this fact we consider the divergences in some nonequilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of renormalization of such divergences and illustrate it with some simple examples. The fact that the system is non ergodic leads to the following consequence: to prove that the system tends to the thermal equilibrium we should take into account its behavior on its boundary. In this paper we illustrate this thesis with the Bogoliubov derivation of the kinetic equations.