Atomic Theory of Collective Excitations in Bose-Einstein Condensation and Spontaneously Broken Gauge Symmetry

TL;DR

This paper develops a quantum Hamilton-Jacobi based theory for collective excitations in Bose-Einstein condensates, revealing surface behavior, phonon spectra, and the classical limit of hard spheres, linking superfluidity and symmetry breaking.

Contribution

It introduces a novel theoretical framework combining quantum Hamilton-Jacobi and phase coherence to analyze excitations in Bose-Einstein condensates, including surface effects and phonon spectra.

Findings

Free surface behaves like a normal fluid, indicating superfluid breakdown.

Phonon spectrum inside the surface follows a linear dispersion scaled by external potential.

Hard spheres collapse to a classical lattice with zero-point vibrations as scattering length approaches zero.

Abstract

A theory of collective excitations in Bose-Einstein condensation in a trap is developed based on the quantum Hamilton-Jacobi equation of Bohm and the phase coherence along with the idea of off-diagonal long range order of Penrose and Onsager. First, we show that a free surface behaves like a normal fluid - a breakdown of superfluidity. Second, inside the free surface it is shown that the spectrum of phonons is of the form $\omega=ck$ scaled with the external potential, where the speed of (first) sound, $c=[4\pi a\rho\hbar^{2}]^{1/2}/M$ and $k$ is the wave number. Third, in the limit $a\to 0$, the hard spheres in the Bose-Einstein condensation collapse to a close-packed classical lattice with the zero-point vibrational motion about fixed points.