Eur. Phys. J. B 23, 87-96 (2001)
https://doi.org/10.1007/s100510170085

Mean-field theory of quantum Brownian motion

¹ CEA/Saclay, Service de Physique Théorique, 91191 Gif-sur-Yvette Cedex, France
² Yerevan Physics Institute, Alikhanian Brothers St. 2, Yerevan 375036, Armenia
³ Department of Physics and Astronomy, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

Corresponding author: ^a aarmen@moon.yerphi.am

Received: 20 February 2001
Revised: 12 June 2001
Published online: 15 September 2001

Abstract

We investigate a mean-field approach to a quantum Brownian particle interacting with a quantum thermal bath at temperature T, and subjected to a non-linear potential. An exact, partially classical description of quantum Brownian motion is proposed, which uses negative probabilities in its intermediate steps. It is shown that properties of the quantum particle can be mapped to those of two classical Brownian particles in a common potential, where one of them interacts with the quantum bath, whereas another one interacts with a classical bath at zero temperature. Due to damping the system allows a unique and non-singular classical limit at n->0. For high T the stationary state becomes explicitly classical. The low-temperature case is studied through an effective Fokker-Planck equation. Non-trivial purely quantum correlation effects between the two particles are found.