Towards nonlinear quantum Fokker-Planck equations

Details Towards nonlinear quantum Fokker-Planck equations Towards nonlinear quantum Fokker-Planck equations

2008-08-04

arxiv.org/abs/0808.0326v4

Int. J. Theor. Phys. 48 (2009) 1431-1435

Physics

Quantum Physics

Scientific paper

10.1007/s10773-008-9913-9

It is demonstrated how the equilibrium semiclassical approach of Coffey et al. can be improved to describe more correctly the evolution. As a result a new semiclassical Klein-Kramers equation for the Wigner function is derived, which remains quantum for a free quantum Brownian particle as well. It is transformed to a semiclassical Smoluchowski equation, which leads to our semiclassical generalization of the classical Einstein law of Brownian motion derived before. A possibility is discussed how to extend these semiclassical equations to nonlinear quantum Fokker-Planck equations based on the Fisher information.

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