Accelerating analysis of Boltzmann equations using Gaussian mixture models: Application to quantum Bose-Fermi mixtures

TL;DR

This paper introduces a Gaussian mixture model approach to efficiently solve Boltzmann equations, enabling detailed analysis of collective modes in quantum Bose-Fermi mixtures relevant to cold atom experiments.

Contribution

The paper presents a novel Gaussian mixture model method that reduces computational costs in solving Boltzmann equations for complex quantum many-body systems.

Findings

Interference effects between bosonic and fermionic modes observed

Damping of collective modes characterized

Hydrodynamic behavior identified in certain regimes

Abstract

The Boltzmann equation is a powerful theoretical tool for modeling the collective dynamics of quantum many-body systems subject to external perturbations. Analysis of the equation gives access to linear response properties including collective modes and transport coefficients, but often proves intractable due to computational costs associated with multidimensional integrals describing collision processes. Here, we present a method to resolve this bottleneck, enabling the study of a broad class of many-body systems that appear in fundamental science contexts and technological applications. Specifically, we demonstrate that a Gaussian mixture model can accurately represent equilibrium distribution functions, thereby allowing efficient evaluation of collision integrals. Inspired by cold atom experiments, we apply this method to investigate the collective behavior of a quantum Bose-Fermi mixture of cold atoms in a cigar-shaped trap, a system that is particularly challenging to analyze. We focus on monopole and quadrupole collective modes above the Bose-Einstein transition temperature, and find a rich phenomenology that spans interference effects between bosonic and fermionic collective modes, dampening of these modes, and the emergence of hydrodynamics in various parameter regimes. These effects are readily verifiable experimentally.