A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation

TL;DR

This paper introduces a new Monte Carlo method for modeling thermal damping that overcomes limitations of the standard Brownian motion master equation by ensuring complete positivity and enabling efficient simulations.

Contribution

It presents a stochastic Schrödinger equation approach that models quantum Brownian motion without extra diffusion, improving accuracy for nonlinear systems.

Findings

The new SSE is completely positive and efficiently solvable.

It captures nonlinear effects better than traditional master equations.

Applicable to nonlinear damping scenarios.

Abstract

The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term that generates additional position diffusion. He we show that one can obtain a completely positive simple quantum Brownian motion, efficiently solvable, without any extra diffusion. This is achieved by using a stochastic Schroedinger equation (SSE), closely analogous to Langevin's equation, that has no equivalent Markovian master equation. Considering a specific example, we show that this SSE is sensitive to nonlinearities in situations in which the master equation is not, and may therefore be a better model of damping for nonlinear systems.