Stochastic simulations of fermionic dynamics with phase-space representations

TL;DR

This paper explores phase-space simulation methods for fermionic quantum dynamics using Gaussian operator bases, demonstrating how to optimize stochastic differential equations for longer simulation times in ultra-cold molecular gas dissociation.

Contribution

It introduces a tailored Gaussian phase-space approach for simulating fermionic dynamics, analyzing how different mappings affect simulation accuracy and duration.

Findings

The Gaussian phase-space method can accurately simulate fermionic dynamics.

Choice of stochastic mapping influences simulation stability and duration.

Application to ultra-cold molecular gas dissociation demonstrates practical utility.

Abstract

A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples.