Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique

TL;DR

This paper develops a rigorous, numerically efficient framework using the Projection Operator Technique to derive evolution equations for momentum distribution and correlations in weakly interacting quantum systems, validated against 1D models.

Contribution

It introduces a novel, rigorous method to derive and numerically solve equations governing out-of-equilibrium quantum dynamics, extending previous approaches.

Findings

Excellent agreement with known 1D model results

Efficient numerical solution of derived equations

Framework applicable to weakly interacting quantum systems

Abstract

We present a rigorous framework to obtain evolution equations for the momentum distribution and higher order correlation functions in weakly interacting systems based on the Projection Operator Technique. These equations can be numerically solved in an efficient way. We compare the solution of the equations with known results for 1D models and find an excellent agreement.