Representative statistical ensembles for Bose systems with broken gauge symmetry

TL;DR

This paper develops a consistent statistical ensemble framework for Bose-condensed systems with broken gauge symmetry, resolving longstanding issues of nonconservation and spectral gaps in existing theories.

Contribution

It introduces the concept of representative ensembles that incorporate all system constraints, ensuring a self-consistent, conserving, and gapless description of Bose systems.

Findings

Removes paradoxes in Bose-condensed systems

Ensures theories are both conserving and gapless

Provides a self-consistent framework for equilibrium Bose systems

Abstract

Bose-condensed systems with broken global gauge symmetry are considered. The description of these systems, as has been shown by Hohenberg and Martin, possesses an internal inconsistency, resulting in either nonconserving theories or yielding an unphysical gap in the spectrum. The general notion of representative statistical ensembles is formulated for arbitrary statistical systems, equilibrium or not. The principal idea of this notion is the necessity of taking into account all imposed conditions that uniquely define the given statistical system. Employing such a representative ensemble for Bose-condensed systems removes all paradoxes, yielding a completely self-consistent theory, both conserving and gapless in any approximation. This is illustrated for an equilibrium uniform Bose system.