---
_id: '2731'
abstract:
- lang: eng
text: We study the time evolution of a quantum particle in a Gaussian random environment.
We show that in the weak coupling limit the Wigner distribution of the wave function
converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann
collision kernel is given by the Born approximation of the quantum differential
scattering cross section.
acknowledgement: Partially supported by U.S. National Science Foundation grants DMS-9403462,
9703752. We would like to thank H. Spohn for his several comments and discussions
on this project. Part of this work was done during the time when L. E. visited the
Erwin Schrödinger Institute in Vienna and when both authors visited the Center of
Theoretical Sciences in Taiwan. We thank them for the hospitality and the support
of this work.
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
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. Linear Boltzmann equation as the weak coupling limit of a random
Schrödinger equation. *Communications on Pure and Applied Mathematics*. 2000;53(6):667-735.
doi:10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
apa: Erdös, L., & Yau, H. (2000). Linear Boltzmann equation as the weak coupling
limit of a random Schrödinger equation. *Communications on Pure and Applied
Mathematics*. Wiley-Blackwell. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
chicago: Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling
Limit of a Random Schrödinger Equation.” *Communications on Pure and Applied
Mathematics*. Wiley-Blackwell, 2000. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5.
ieee: L. Erdös and H. Yau, “Linear Boltzmann equation as the weak coupling limit
of a random Schrödinger equation,” *Communications on Pure and Applied Mathematics*,
vol. 53, no. 6. Wiley-Blackwell, pp. 667–735, 2000.
ista: Erdös L, Yau H. 2000. Linear Boltzmann equation as the weak coupling limit
of a random Schrödinger equation. Communications on Pure and Applied Mathematics.
53(6), 667–735.
mla: Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling
Limit of a Random Schrödinger Equation.” *Communications on Pure and Applied
Mathematics*, vol. 53, no. 6, Wiley-Blackwell, 2000, pp. 667–735, doi:10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5.
short: L. Erdös, H. Yau, Communications on Pure and Applied Mathematics 53 (2000)
667–735.
date_created: 2018-12-11T11:59:18Z
date_published: 2000-06-01T00:00:00Z
date_updated: 2023-05-03T09:09:04Z
day: '01'
doi: 10.1002/(SICI)1097-0312(200006)53:6<667::AID-CPA1>3.0.CO;2-5
extern: '1'
external_id:
arxiv:
- math-ph/9901020
intvolume: ' 53'
issue: '6'
language:
- iso: eng
month: '06'
oa_version: Preprint
page: 667 - 735
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- 0010-3640
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4161'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Linear Boltzmann equation as the weak coupling limit of a random Schrödinger
equation
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 53
year: '2000'
...