---
_id: '2711'
abstract:
- lang: eng
  text: We study the long 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 the solution of a linear Boltzmann equation globally
    in time. The Boltzmann collision kernel is given by the Born approximation of
    the quantum scattering cross section.
alternative_title:
- 'Operator Theory: Advances and Applications'
article_processing_charge: No
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 weak coupling limit of the random
    Schrödinger equation. In: <i>Proceedings of the 7th QMath Conference</i>. Vol
    108. World Scientific Publishing; 1999:233-242. doi:<a href="https://doi.org/10.1007/978-3-0348-8745-8_20">10.1007/978-3-0348-8745-8_20</a>'
  apa: 'Erdös, L. (1999). Linear Boltzmann equation as the weak coupling limit of
    the random Schrödinger equation. In <i>Proceedings of the 7th QMath Conference</i>
    (Vol. 108, pp. 233–242). Prague, Czech Republik: World Scientific Publishing.
    <a href="https://doi.org/10.1007/978-3-0348-8745-8_20">https://doi.org/10.1007/978-3-0348-8745-8_20</a>'
  chicago: Erdös, László. “Linear Boltzmann Equation as the Weak Coupling Limit of
    the Random Schrödinger Equation.” In <i>Proceedings of the 7th QMath Conference</i>,
    108:233–42. World Scientific Publishing, 1999. <a href="https://doi.org/10.1007/978-3-0348-8745-8_20">https://doi.org/10.1007/978-3-0348-8745-8_20</a>.
  ieee: L. Erdös, “Linear Boltzmann equation as the weak coupling limit of the random
    Schrödinger equation,” in <i>Proceedings of the 7th QMath Conference</i>, Prague,
    Czech Republik, 1999, vol. 108, pp. 233–242.
  ista: 'Erdös L. 1999. Linear Boltzmann equation as the weak coupling limit of the
    random Schrödinger equation. Proceedings of the 7th QMath Conference. QMath: Mathematical
    Results in Quantum Physics, Operator Theory: Advances and Applications, vol. 108,
    233–242.'
  mla: Erdös, László. “Linear Boltzmann Equation as the Weak Coupling Limit of the
    Random Schrödinger Equation.” <i>Proceedings of the 7th QMath Conference</i>,
    vol. 108, World Scientific Publishing, 1999, pp. 233–42, doi:<a href="https://doi.org/10.1007/978-3-0348-8745-8_20">10.1007/978-3-0348-8745-8_20</a>.
  short: L. Erdös, in:, Proceedings of the 7th QMath Conference, World Scientific
    Publishing, 1999, pp. 233–242.
conference:
  end_date: 1999-09-26
  location: Prague, Czech Republik
  name: 'QMath: Mathematical Results in Quantum Physics'
  start_date: 1998-06-22
date_created: 2018-12-11T11:59:12Z
date_published: 1999-01-01T00:00:00Z
date_updated: 2022-09-13T08:02:52Z
day: '01'
doi: 10.1007/978-3-0348-8745-8_20
extern: '1'
intvolume: '       108'
language:
- iso: eng
month: '01'
oa_version: None
page: 233 - 242
publication: Proceedings of the 7th QMath Conference
publication_identifier:
  isbn:
  - '9783034897549'
publication_status: published
publisher: World Scientific Publishing
publist_id: '4185'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Linear Boltzmann equation as the weak coupling limit of the random Schrödinger
  equation
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 108
year: '1999'
...