Erdos L., Yau H.-T.
Linear Boltzmann Equation as the Weak Coupling Limits of
a Random Schrodinger Equation
(1114K, .ps file)
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.
The current version extends our previous result to include
the two dimensional case as well.