Many-body physics in the classical-field description of a degenerate Bose gas

TL;DR

This paper extends the classical-field formalism for finite-temperature Bose gases to include anomalous correlations without symmetry-breaking, providing a comprehensive description of many-body effects and fluctuations in degenerate Bose gases.

Contribution

It introduces U(1)-symmetric classical-field variables for calculating anomalous correlations, advancing the understanding of many-body processes in Bose gases without symmetry-breaking assumptions.

Findings

Classical-field dynamics incorporate many-body effects modifying mean-field potentials.

The method quantifies the anomalous and non-Gaussian character of field fluctuations.

Results support the Penrose-Onsager definition of the condensate orbital in equilibrium.

Abstract

The classical-field formalism has been widely applied in the calculation of normal correlation functions, and the characterization of condensation, in finite-temperature Bose gases. Here we discuss the extension of this method to the calculation of more general correlations, including the so-called anomalous correlations of the field, without recourse to symmetry-breaking assumptions. Our method is based on the introduction of U(1)-symmetric classical-field variables analogous to the modified quantum ladder operators of number-conserving approaches to the degenerate Bose gas, and allows us to rigorously quantify the anomalous and non-Gaussian character of the field fluctuations. We compare our results for anomalous correlation functions with the predictions of mean-field theories, and demonstrate that the nonlinear classical-field dynamics incorporate a full description of many-body processes which modify the effective mean-field potentials experienced by condensate and noncondensate atoms. We discuss the role of these processes in shaping the condensate mode, and thereby demonstrate the consistency of the Penrose-Onsager definition of the condensate orbital in the classical-field equilibrium. We consider the contribution of various noncondensate-field correlations to the overall suppression of density fluctuations and interactions in the field, and demonstrate the distinct roles of phase and density fluctuations in the transition of the field to the normal phase.