Equilibrium, Relaxation and Fluctuations in homogeneous Bose-Einstein Condensates: Linearized Classical Field Analysis

TL;DR

This paper analyzes the linearized stochastic projected Gross-Pitaevskii equation for finite-temperature Bose-Einstein condensates, focusing on equilibrium, relaxation, and fluctuations, and emphasizes the importance of energy damping in decay processes.

Contribution

It provides an optimal cut-off choice for dividing the Bose gas and highlights the significance of energy damping and scattering in BEC dynamics, extending analysis beyond linear approximations.

Findings

Close agreement between linearized and full non-linear SPGPE simulations

Reveals the importance of energy damping in BEC decay processes

Analyzes equilibrium and fluctuations in homogeneous BECs across dimensions

Abstract

Open quantum systems theory is central to describing the dynamics and equilibration of dilute-gas Bose-Einstein condensates (BECs). We present an analysis of the linearized stochastic projected Gross-Pitaevskii equation (SPGPE) describing finite-temperature BECs. Our treatment provides an optimal choice for the cut-off that divides the Bose gas into the low-energy coherent region forming a classical wave, and the high-energy thermal cloud treated as a reservoir. Moreover, it highlights the relevance of energy damping, the number-conserving scattering between thermal and coherent atoms. We analyze the equilibrium properties and near-equilibrium relaxation of a homogeneous BEC in one, two and three dimensions at high phase-space density, and calculate the autocorrelation function and power spectrum of the density and phase fluctuations. Simulations of the full non-linear SPGPE are in close agreement, and extend our arguments beyond the linear regime. Our work suggests the need for a re-examination of decay processes in BECs studied under the neglect of energy damping.