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Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions | | Suman Kumar Banik
; Bidhan Chandra Bag
; Deb Shankar Ray
; | | Date: |
11 Mar 2002 | | Journal: | Phys. Rev. E 65, 051106 (2002) | | Subject: | Quantum Physics; Statistical Mechanics; Chemical Physics | quant-ph cond-mat.stat-mech physics.chem-ph | | Abstract: | Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {it exact} quantum analogues of their classical counterparts. The present work is {it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit). | | Source: | arXiv, quant-ph/0203040 | | Other source: | [GID 1044455] pmid12059528 | | Services: | Forum | Review | PDF | Favorites | |
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