Author(s):

Erdős, László; Yau, HorngTzer

Article Title: 
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation

Affiliation 

Abstract: 
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.

Journal Title:

Communications on Pure and Applied Mathematics

Volume: 
53

Issue 
6

ISSN:

10970312

Publisher:

WileyBlackwell

Date Published:

20000601

Start Page: 
667

End Page:

735

DOI: 
10.1002/(SICI)10970312(200006)53:6<667::AIDCPA1>3.0.CO;25

Open access: 
no 