Spontaneously broken gauge symmetry in a Bose gas with constant particle number

TL;DR

This paper investigates how spontaneous gauge symmetry breaking occurs in a Bose gas with fixed particle number, revealing it as a non-local process affecting the phase relations between condensate and non-condensate components.

Contribution

It demonstrates that spontaneous symmetry breaking in such systems is a non-local phenomenon within the Hilbert space, while the total particle number and global gauge symmetry are conserved.

Findings

Symmetry breaking appears as a non-local process in position space.

The relative phase distribution between condensate and non-condensate fields is key.

Global U(1) symmetry remains preserved due to fixed particle number.

Abstract

The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose-Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.