Issue
EPL
Volume 85, Number 4, February 2009
Article Number 40002
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/85/40002
Published online 16 February 2009
EPL, 85 (2009) 40002
DOI: 10.1209/0295-5075/85/40002

A Monte Carlo method for modeling thermal damping: Beyond the Brownian motion master equation

K. Jacobs

Department of Physics, University of Massachusetts at Boston - 100 Morrissey Blvd, Boston, MA 02125, USA

kjacobs@cs.umb.edu

received 4 September 2008; accepted in final form 26 January 2009; published February 2009
published online 16 February 2009

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 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