Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation

Details Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation

1999-01-25

arxiv.org/abs/math-ph/9901020v1

Physics

Mathematical Physics

8 figures plus a style file called nume2.tex

Scientific paper

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.

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