Stochastic simulation algorithm for the quantum linear Boltzmann equation

TL;DR

This paper introduces a Monte Carlo wave function algorithm for efficiently simulating the quantum linear Boltzmann equation, enabling detailed analysis of quantum particle dynamics in a gas environment.

Contribution

It presents a novel stochastic simulation method for the quantum linear Boltzmann equation, including extensions to superposition states and various physical limits.

Findings

Validated the algorithm against known limits like quantum Brownian motion

Demonstrated the method's ability to simulate superposition decoherence

Provided insights into gas-particle interaction effects

Abstract

We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The algorithm leads to a numerically efficient stochastic simulation procedure for the most general form of this integro-differential equation, which involves a five-dimensional integral over microscopically defined scattering amplitudes that account for the gas interactions in a non-perturbative fashion. The simulation technique is used to assess various limiting forms of the quantum linear Boltzmann equation, such as the limits of pure collisional decoherence and quantum Brownian motion, the Born approximation and the classical limit. Moreover, we extend the method to allow for the simulation of the dissipative and decohering dynamics of superpositions of spatially localized wave packets, which enables the study of many physically relevant quantum phenomena, occurring e.g. in the interferometry of massive particles.