Abstract
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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Tsekov, R. Towards Nonlinear Quantum Fokker-Planck Equations. Int J Theor Phys 48, 1431–1435 (2009). https://doi.org/10.1007/s10773-008-9913-9
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DOI: https://doi.org/10.1007/s10773-008-9913-9