Non-Abelian linear Boltzmann equation and quantum correction to Kramers and Smoluchowski equation
A quantum linear Boltzmann equation, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with, is proposed. Due to this operator structure it is a non-Abelian linear Boltzmann equation and when expressed through the Wigner f...
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| Published in: | Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Vol. 66; no. 2 Pt 2; p. 027107 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01-08-2002
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| Online Access: | Get full text |
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| Summary: | A quantum linear Boltzmann equation, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with, is proposed. Due to this operator structure it is a non-Abelian linear Boltzmann equation and when expressed through the Wigner function it allows for a direct comparison with the classical one. Considering a Brownian particle, the corresponding Fokker-Planck equation is obtained in a most direct way taking the limit of small energy and momentum transfer. A typical quantum correction to the Kramers equation thus appears, describing diffusion in position and further implying a correction to Einstein's diffusion coefficient in the high temperature and friction limit in which the Smoluchowski equation emerges. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1539-3755 1063-651X 1095-3787 |
| DOI: | 10.1103/PhysRevE.66.027107 |