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

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.

C-Field Methods for Non-Equilibrium Bose Gases

“…However, dynamical calculations within a pure PGPE formalism are able to provide useful insights into the dynamics of degenerate Bose-gas systems in situations where a precise identification of the method with the full field theory is impractical [45,58,66]. The PGPE has also been used to establish the connection between c-field methods and more traditional theoretical methods based on U(1) symmetry breaking [61,67].…”

Anomalous density for Bose gases at finite temperature

“…Yukalov [42] adopted a quite different approach by using the notion of representative statistical ensembles. Recently, Wright et al [43,44] have used the classical-field trajectories of the Projected Gross-Pitaevskii equation.…”

Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

“…At low to moderate temperatures generalised mean field theories have been developed, and successfully modelled a number of experimental scenarios. The Zaremba-Nikuni-Griffin (ZNG) [28][29][30][31][32][33], projected Gross-Pitaevskii equation (PGPE) [34][35][36][37][38][39][40][41][42][43][44] (including applications to spinor condensates [45,46]), and number conserving [47][48][49] theories each have advantages for describing BEC evolution, namely, relative ease of handling thermal cloud dynamics, inclusion of many appreciably populated coherent modes, and inclusion of off-diagonal long range order, respectively. At temperatures well below the BEC transition (T c ), these effects are essential aspects of finite-temperature BEC physics.…”