Linear Boltzmann equation as the weak coupling limit of a random Schrodinger equation

Authors
Erdos, L Yau, HT
Citation
L. Erdos et Ht. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrodinger equation, COM PA MATH, 53(6), 2000, pp. 667-735
Citations number
9
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN journal
00103640 → ACNP
Volume
53
Issue
6
Year of publication
2000
Pages
667 - 735
Database
ISI
SICI code
0010-3640(200006)53:6<667:LBEATW>2.0.ZU;2-Z
Abstract
We study the time evolution of a quantum particle in a Gaussian random envi ronment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation g lobally in time. The Boltzmann collision kernel is given by the Born approx imation of the quantum differential scattering cross section. (C) 2000 John Wiley & Sons, Inc.