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.
|Titolo:||Non-Abelian linear Boltzmann equation and quantum correction to Kramers and Smoluchowski equation|
VACCHINI, BASSANO MARIA (Primo)
|Settore Scientifico Disciplinare:||Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici|
|Data di pubblicazione:||2002|
|Digital Object Identifier (DOI):||10.1103/PhysRevE.66.027107|
|Appare nelle tipologie:||01 - Articolo su periodico|