Nonperturbative dynamical many-body theory of a Bose-Einstein condensate

TL;DR

This paper introduces a non-perturbative dynamical many-body theory for strongly interacting Bose gases, capturing effects beyond mean-field and perturbative approaches, and analyzes their non-equilibrium evolution.

Contribution

It develops a systematic non-perturbative expansion for quantum gases, enabling the study of dynamics beyond mean-field approximations.

Findings

The theory captures direct scattering, memory, and off-shell effects.

Homogeneous 1D Bose gases evolve to non-equilibrium quasistationary states.

Approach to thermal equilibrium is extremely slow.

Abstract

A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory and ``off-shell'' effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a non-equilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.