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

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

2008-07-26

arxiv.org/abs/0807.4211v3

EPL 85, 40002 (2009)

Physics

Quantum Physics

6 pages, revtex4. v2: numerical results for a nonlinear system

Scientific paper

10.1209/0295-5075/85/40002

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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