---
_id: '2695'
abstract:
- lang: eng
  text: 'We study a quantum particle in a random potential in two scaling limits:
    the low density limit (or Boltzman-Grad) and the weak coupling limit. The low
    density limit is the quantum analogue of the Lorentz gas. In both cases, the phase
    space density of the quantum evolution defined through the Wigner transform or
    the Husimi function converges weakly to a linear Boltz-mann equation with collision
    kernel given by the quantum scattering cross section. '
alternative_title:
- Contemporary Mathematics
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
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
citation:
  ama: 'Erdös L, Yau H. Linear Boltzmann equation as scaling limit of quantum Lorentz
    gas. In: <i>Advances in Differential Equations and Mathematical Physics</i>. Vol
    217. American Mathematical Society; 1998:137-155. doi:<a href="https://doi.org/10.1090/conm/217">10.1090/conm/217</a>'
  apa: Erdös, L., &#38; Yau, H. (1998). Linear Boltzmann equation as scaling limit
    of quantum Lorentz gas. In <i>Advances in Differential Equations and Mathematical
    Physics</i> (Vol. 217, pp. 137–155). American Mathematical Society. <a href="https://doi.org/10.1090/conm/217">https://doi.org/10.1090/conm/217</a>
  chicago: Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit
    of Quantum Lorentz Gas.” In <i>Advances in Differential Equations and Mathematical
    Physics</i>, 217:137–55. American Mathematical Society, 1998. <a href="https://doi.org/10.1090/conm/217">https://doi.org/10.1090/conm/217</a>.
  ieee: L. Erdös and H. Yau, “Linear Boltzmann equation as scaling limit of quantum
    Lorentz gas,” in <i>Advances in Differential Equations and Mathematical Physics</i>,
    vol. 217, American Mathematical Society, 1998, pp. 137–155.
  ista: 'Erdös L, Yau H. 1998.Linear Boltzmann equation as scaling limit of quantum
    Lorentz gas. In: Advances in Differential Equations and Mathematical Physics.
    Contemporary Mathematics, vol. 217, 137–155.'
  mla: Erdös, László, and Horng Yau. “Linear Boltzmann Equation as Scaling Limit of
    Quantum Lorentz Gas.” <i>Advances in Differential Equations and Mathematical Physics</i>,
    vol. 217, American Mathematical Society, 1998, pp. 137–55, doi:<a href="https://doi.org/10.1090/conm/217">10.1090/conm/217</a>.
  short: L. Erdös, H. Yau, in:, Advances in Differential Equations and Mathematical
    Physics, American Mathematical Society, 1998, pp. 137–155.
date_created: 2018-12-11T11:59:07Z
date_published: 1998-01-01T00:00:00Z
date_updated: 2022-08-31T11:46:40Z
day: '01'
doi: 10.1090/conm/217
extern: '1'
intvolume: '       217'
language:
- iso: eng
month: '01'
oa_version: None
page: 137 - 155
publication: Advances in Differential Equations and Mathematical Physics
publication_identifier:
  issn:
  - 0271-4132
publication_status: published
publisher: American Mathematical Society
publist_id: '4202'
quality_controlled: '1'
status: public
title: Linear Boltzmann equation as scaling limit of quantum Lorentz gas
type: book_chapter
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 217
year: '1998'
...