Physical aspects of symmetry breaking in Bose gases at thermal equilibrium

TL;DR

This paper introduces a numerical quantum field model for Bose gases that explains symmetry breaking and phase coherence phenomena at thermal equilibrium, linking quantum field dynamics to observable physical symmetry changes.

Contribution

It presents a novel two-dimensional non-local order parameter model that captures wave-like correlations and explains symmetry aspects in weakly interacting Bose gases at equilibrium.

Findings

Model explains symmetry breaking as a global physical process.

Links quantum coherence time to phase gauge symmetry.

Describes time propagation as convergence to Boltzmann equilibrium.

Abstract

The theory of non-interacting Bose gases is supplemented by a numerical quantum field description with a two-dimensional non-local order parameter that allows the modeling of wave-like atomic correlations and interference effects in the limit of low atomic densities. From the present model, it is possible to explain symmetry aspects of non-interacting and very weakly interacting Bose gases in the limit of fluctuating particle numbers, like the forward propagation of time and the relation to the breaking and preservation of phase gauge symmetry in solids. In the present formalism, the propagation of one-directional time arises from the pre-defined and equivalent convergence of independent quantum fields towards the Boltzmann equilibrium, and it is shown that Glauber coherent states are related to the definition of the quantized field. Coherently coupling condensate and non-condensate parts as a direct consequence of the increasing quantum coherence time between the different quantum field components in the Bose gas from cooling to below the critical temperature, the present model describes symmetry breaking, which is originally known from the definition of a specific gauge field from Elitzur's theorem for local gauge fields, as a global physical rather than a purely formal mathematical process.