A Monte Carlo method for modeling thermal damping: Beyond the Brownian motion master equationK. Jacobs
Department of Physics, University of Massachusetts at Boston - 100 Morrissey Blvd, Boston, MA 02125, USA
received 4 September 2008; accepted in final form 26 January 2009; published February 2009
published online 16 February 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.
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.
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