Coherent Collective Excitations in a Superfluid: Spontaneously Broken Symmetries and Fluctuations-Dissipation

TL;DR

This paper develops an elementary theoretical framework for understanding phase-coherent collective excitations in superfluids and Bose-Einstein condensates, emphasizing broken symmetries and their physical manifestations.

Contribution

It introduces a unified theory of broken symmetry and collective excitations in superfluid helium and trapped Bose gases, explaining long-standing phenomena.

Findings

Broken symmetry occurs at the surface layer of inhomogeneous Bose systems.

The theory explains the shell-like structure of Bose-Einstein condensation in traps.

It provides a coherent explanation for longstanding puzzles in superfluid helium.

Abstract

This paper presents an elementary theory of the phase-coherent collective excitations in both He II in the gravitational field and atomic Bose-Einstein condensation in a trap. The theory is based on the concept of off-diagonal long-range order by Penrose and Onsager and the quantum theory of Bohm, with emphasis on the broken symmetry in a Bose-Einstein gas with repulsive interactions. It is shown that a spontaneously broken symmetry that accompanies a phonon (Nambu-Goldstone mode) takes place at the surface layer of an inhomogeneous Bose system in the presence of an external field. The spontaneously broken symmetry in a Bose system is described and is shown to manifest itself in both He II and the Bose-Einstein condensation - a shell-like structure of Bose-Einstein condensation in a trap. The broken symmetry gives a coherent explanation for a number of long standing puzzles in He II.