Initial-Value Problem for Inhomogeneous Condensate: Gaussian Approximation and Beyond

TL;DR

This paper develops a set of exact kinetic equations for inhomogeneous condensates using many-body theory, illustrating the approach with phi^4 field theory in 1+1 dimensions, and introduces a systematic mean-field expansion beyond the Gaussian approximation.

Contribution

It introduces a formalism for deriving kinetic equations for inhomogeneous condensates and extends the Gaussian approximation with dynamical correlation effects.

Findings

Derivation of exact kinetic equations for inhomogeneous condensates

Systematic mean-field expansion including Gaussian and correlation effects

Application to phi^4 field theory in 1+1 dimensions

Abstract

Using many-body theory we develop a set of formally exact kinetic equations for inhomogeneous condensate and one-body observables. The method is illutrated for phi^4 field theory in 1+1 dimensions. These equations, when computed with the help of time-dependent projection technique, lead to a systematic mean-field expansion. The lowest and the higher order terms correspond to, respectively, the gaussian approximation and the dynamical correlation effect.