Volume 85, Number 4, February 2009
|Number of page(s)||6|
|Published online||16 February 2009|
A Monte Carlo method for modeling thermal damping: Beyond the Brownian motion master equation
Department of Physics, University of Massachusetts at Boston - 100 Morrissey Blvd, Boston, MA 02125, USA
Corresponding author: email@example.com
Accepted: 26 January 2009
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 Schrödinger 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.
PACS: 05.40.Jc – Brownian motion / 03.65.Yz – Decoherence; open systems; quantum statistical methods / 85.85.+j – Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
© EPLA, 2009
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