A Nonequilibrium Quantum Field Theory Description of the Bose-Einstein Condensate

TL;DR

This paper develops a nonequilibrium quantum field theory framework to analyze the time evolution of a homogeneous Bose-Einstein condensate, revealing the importance of interactions and identifying distinct regimes in momentum space.

Contribution

It introduces a detailed microscopic model using a nonrelativistic quantum field approach to describe out-of-equilibrium dynamics of Bose-Einstein condensates, highlighting interaction effects and regime distinctions.

Findings

Interaction between fluctuations is crucial for instability.

Two regimes in momentum space with a crossover at a specific energy scale.

Coupled equations fully determine condensate dynamics based on temperature and density.

Abstract

We study the detailed out of equilibrium time evolution of a homogeneous Bose-Einstein condensate.We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the Bose-Einstein condensate. This approach yields the following main results:(i) the interaction between fluctuations proves to be crucial in the mechanism of instability generation; (ii) there are essentially two regimes in the $k$-space, with a crossover for $k^2/2m \sim 2\lambda |\phi_0|^2$, where, in our notation, $\lambda$ is the coupling constant and $|\phi_0|^2$ is the condensate density; (iii) a set of coupled equations that determines completely the nonequilibrium dynamics of the condensate density as a function of the temperature and of the total density of the gas.