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

By Kurt Jacobs


PACS 03.65.Yz – Decoherence; open systems; quantum statistical methods PACS 03.65.Ta – Foundations of quantum mechanics; measurement theory PACS 85.85.+j – Micro- and nano-electromechanical systems (MEMS/NEMS) and devices 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. All mechanical oscillators experience frictional damping, in which they lose energy to their environment. This damping is accompanied by thermalization of the oscillator

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