The Beliaev Broken Symmetry Description of Superfluidity vs the Classical-Field Approach

TL;DR

This paper compares the Beliaev broken symmetry theory and the classical-field approach for superfluidity in Bose systems, highlighting their differences, limitations, and potential for simplifying calculations.

Contribution

It clarifies the conceptual differences between the Beliaev and c-field approaches and discusses how the classical treatment can aid calculations within the broken symmetry formalism.

Findings

The c-field approach has conceptual problems as a superfluidity description.

The classical treatment of low-energy excitations can simplify Beliaev formalism calculations.

The Beliaev approach remains more consistent for describing Bose superfluidity.

Abstract

The standard theoretical basis for understanding superfluidity in Bose systems was formulated by Beliaev in 1957, based on splitting the quantum field operator into a macroscopically occupied condensate component and a non-condensate component. This leads to a description of the condensate in terms of a 'single-particle state', the so-called macroscopic wavefunction. Since the discovery of Bose-condensed gases, an alternative theoretical picture has been developed which is based on a 'coherent band' of classically occupied states. This is often called the classical or c-field approach. The goal of this chapter is to review the differences between the Beliaev broken symmetry and c-field approach, and to argue that the c-field concept of a coherent condensate band of states has problems as a description of Bose superfluidity. However, the c-field idea of treating the lowest energy excitations classically can be used to advantage to simplify calculations within the Beliaev broken-symmetry formalism.