Reconciling the classical-field method with the Beliaev broken-symmetry approach

Wright, TM; Davis, MJ; Proukakis, NP

doi:10.1142/9781848168121_0019

Reconciling the classical-field method with the Beliaev broken-symmetry approach

Lookup NU author(s): Professor Nikolaos Proukakis ORCiD

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Abstract

We present our views on the issues raised in the previous chapter by Griffin and Zaremba. We review some of the strengths and limitations of the Bose symmetry-breaking assumption, and explain how such an approach precludes the description of many important phenomena in degenerate Bose gases. We discuss the theoretical justification for the classical-field (c-field) methods, their relation to other non-perturbative methods for similar systems, and their utility in the description of beyond-mean-field physics. Although it is true that present implementations of c-field methods cannot accurately describe certain collective oscillations of the partially condensed Bose gas, there is no fundamental reason why these methods cannot be extended to treat such scenarios. By contrast, many regimes of non-equilibrium dynamics that can be described with c-field methods are beyond the reach of generalised mean-field kinetic approaches based on symmetry breaking, such as the ZNG formalism.