Atomic Theory of the Two-fluid Model: Broken Gauge Symmetry in Bose-Einstein condensation

TL;DR

This paper derives the dispersion relation for sound waves in a Bose-Einstein condensate, linking broken gauge symmetry at the surface to quantum fluctuations, and aligns with the Bogoliubov spectrum.

Contribution

It introduces an atomic theory connecting broken gauge symmetry with collective excitations in BEC, emphasizing surface effects and quantum fluctuations.

Findings

Dispersion relation matches Bogoliubov phonon spectrum

Broken gauge symmetry occurs at the BEC surface

Surface quantum fluctuations drive symmetry breaking

Abstract

We discuss the collective excitations in a spatially inhomogeneous (cylindrically symmetric) Bose-Einstein condensation (BEC) at low temperature ($T \ll T_{\lambda}$). The main result is the dispersion relation for a (first) sound wave that is obtained by describing the perturbation as a Lagrangian coordinate. The dispersion curve is in good agreement with the Bogoliubov phonon spectrum $\omega=c k$, where $k=k_{\theta}=m/r$, the wave number and $c=[4 \pi a \rho \hbar^{2}]^{1/2}/M$, the speed of first sound. Based on Bohm's quantum theory, a spontaneously broken gauge symmetry in a quantum fluid is discussed in terms of the quantum fluctuation-dissipation, from which it is shown that the symmetry breaking takes place at the free surface of BEC in an external field.