Three-dimensional Monte Carlo simulations of the quantum linear Boltzmann equation

TL;DR

This paper introduces a 3D Monte Carlo simulation method for the quantum Boltzmann equation, enabling analysis of quantum gas dynamics, decoherence, and approach to equilibrium.

Contribution

A novel stochastic wave function algorithm for full three-dimensional Monte Carlo simulations of the quantum Boltzmann equation is developed.

Findings

Studied the approach to equilibrium for various scattering cross sections.

Analyzed higher-order cumulants to identify deviations from Gaussian statistics.

Quantified decoherence times for superpositions of momentum eigenstates.

Abstract

Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full three-dimensional Monte Carlo simulations of this equation. The simulation method is used to study the approach to equilibrium for various scattering cross sections and to determine dynamical deviations from Gaussian statistics through an investigation of higher-order cumulants. Moreover, we examine the loss of coherence of superpositions of momentum eigenstates and determine the corresponding decoherence time scales to quantify the transition from quantum to classical behavior of the state of the test particle.