On Non ergodic Property of Bose Gas with Weak Pair Interaction

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 non equilibrium diagram technique. These divergences are analogous to the divergences in the kinetic equations discovered by Cohen and Dorfman. We develop the general theory of re-normalization of such divergences and illustrate it with some simple examples. The fact that the system is nonergodic 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.