Bose-Einstein Condensation, Fluctuations and Spontaneous Symmetry Breaking

TL;DR

This paper challenges traditional views on Bose-Einstein condensation by proposing a new framework that explains observed fluctuations and symmetry breaking without relying on the Bogoliubov quasi-average method.

Contribution

It introduces an alternative conceptual approach to spontaneous symmetry breaking in Bose-Einstein condensates, emphasizing fluctuation condensation and long-range correlations.

Findings

Fluctuations condense alongside the condensate.

Long-range correlations characterize the symmetry-breaking state.

The Bogoliubov quasi-average method fails to reproduce observed phenomena.

Abstract

The realisation of Bose-Einstein condensation under grand-canonical conditions has provided the experimental evidence for the simultaneous occurrence of macroscopic fluctuations and phase coherence of the condensate. The observation of these two features, against a consolidated tradition which wants the fluctuations to be pathological (grand-canonical catastrophe) and incompatible with spontaneous symmetry braking, calls for a comprehensive rethinking of the approach to the problem. In this paper we consider the uniform ideal gas in a box and we present an alternative conceptual framework. We show that the usually-employed Bogoliubov quasi-average construction fails to reproduce the broken-symmetry state. The observed features are accounted for by a different pattern of spontaneous symmetry breaking, characterised by condensation of fluctuations and long-range correlations of the order parameter.