We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.

Relaxation dynamics of a quantum Brownian particle in an ideal gas / K. Hornberger, B. Vacchini. - In: THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS. - ISSN 1951-6355. - 151:1(2007), pp. 59-72.

Relaxation dynamics of a quantum Brownian particle in an ideal gas

B. Vacchini
Ultimo
2007

Abstract

We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
2007
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/38517
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 17
social impact