Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation
Mathematical Physics
2007-05-23 v1 math.MP
Probability
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.
Cite
@article{arxiv.math-ph/9901020,
title = {Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation},
author = {L. Erdos and H. -T. Yau},
journal= {arXiv preprint arXiv:math-ph/9901020},
year = {2007}
}
Comments
8 figures plus a style file called nume2.tex