---
_id: '2738'
abstract:
- lang: eng
text: We consider the long time evolution of a quantum particle weakly interacting
with a phonon field. We show that in the weak coupling limit the Wigner distribution
of the electron density matrix converges to the solution of the linear Boltzmann
equation globally in time. The collision kernel is identified as the sum of an
emission and an absorption term that depend on the equilibrium distribution of
the free phonon modes.
acknowledgement: "This work initially was a joint project with H.-T. Yau and several
ideas\r\npresented here have been developed in collaboration with him. I would like\r\nto
thank him for the invaluable discussions and encouragement through\r\nthe entire
work. Part of this project was completed during several visits at\r\nthe Erwin Schrödinger
Institute, Vienna, and at the Center of Theoretical\r\nStudies, Hsinchu, Taiwan.
The author is grateful for the hospitality and\r\nfinancial support. This work was
partially supported by NSF Grant DMS9970323."
article_processing_charge: No
article_type: original
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Erdös L. Linear Boltzmann equation as the long time dynamics of an electron
weakly coupled to a phonon field. Journal of Statistical Physics. 2002;107(5-6):1043-1127.
doi:10.1023/A:1015157624384
apa: Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an
electron weakly coupled to a phonon field. Journal of Statistical Physics.
Springer. https://doi.org/10.1023/A:1015157624384
chicago: Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of
an Electron Weakly Coupled to a Phonon Field.” Journal of Statistical Physics.
Springer, 2002. https://doi.org/10.1023/A:1015157624384.
ieee: L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron
weakly coupled to a phonon field,” Journal of Statistical Physics, vol.
107, no. 5–6. Springer, pp. 1043–1127, 2002.
ista: Erdös L. 2002. Linear Boltzmann equation as the long time dynamics of an electron
weakly coupled to a phonon field. Journal of Statistical Physics. 107(5–6), 1043–1127.
mla: Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron
Weakly Coupled to a Phonon Field.” Journal of Statistical Physics, vol.
107, no. 5–6, Springer, 2002, pp. 1043–127, doi:10.1023/A:1015157624384.
short: L. Erdös, Journal of Statistical Physics 107 (2002) 1043–1127.
date_created: 2018-12-11T11:59:20Z
date_published: 2002-06-01T00:00:00Z
date_updated: 2023-07-18T09:08:45Z
day: '01'
doi: 10.1023/A:1015157624384
extern: '1'
external_id:
arxiv:
- math-ph/0108025
intvolume: ' 107'
issue: 5-6
language:
- iso: eng
month: '06'
oa_version: Submitted Version
page: 1043 - 1127
publication: Journal of Statistical Physics
publication_identifier:
issn:
- 0022-4715
publication_status: published
publisher: Springer
publist_id: '4154'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Linear Boltzmann equation as the long time dynamics of an electron weakly coupled
to a phonon field
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 107
year: '2002'
...