dorsal/arxiv
View SchemaGeneralized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions
| Authors | Suman Kumar Banik, Bidhan Chandra Bag, Deb Shankar Ray |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203040 |
| URL | https://arxiv.org/abs/quant-ph/0203040 |
| DOI | 10.1103/PhysRevE.65.051106 |
| Journal | Phys. Rev. E 65, 051106 (2002) |
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).
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"abstract": "Traditionally, the quantum Brownian motion is described by Fokker-Planck or\ndiffusion equations in terms of quasi-probability distribution functions, e.g.,\nWigner functions. These often become singular or negative in the full quantum\nregime. In this paper a simple approach to non-Markovian theory of quantum\nBrownian motion using {\\it true probability distribution functions} is\npresented. Based on an initial coherent state representation of the bath\noscillators and an equilibrium canonical distribution of the quantum mechanical\nmean values of their co-ordinates and momenta we derive a generalized quantum\nLangevin equation in $c$-numbers and show that the latter is amenable to a\ntheoretical analysis in terms of the classical theory of non-Markovian\ndynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski\nequations are the {\\it exact} quantum analogues of their classical\ncounterparts. The present work is {\\it independent} of path integral\ntechniques. The theory as developed here is a natural extension of its\nclassical version and is valid for arbitrary temperature and friction\n(Smoluchowski equation being considered in the overdamped limit).",
"arxiv_id": "quant-ph/0203040",
"authors": [
"Suman Kumar Banik",
"Bidhan Chandra Bag",
"Deb Shankar Ray"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevE.65.051106",
"journal_ref": "Phys. Rev. E 65, 051106 (2002)",
"title": "Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions",
"url": "https://arxiv.org/abs/quant-ph/0203040"
},
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