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arXiv · 0807.4211

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

Kurt Jacobs
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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.

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Kurt Jacobs. 2009-01-06. A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation. https://doi.org/10.1209/0295-5075/85/40002

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