The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

Details The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

2004-12-14

arxiv.org/abs/math-ph/0412044v2

Physics

Mathematical Physics

74 pages, 4 figures, (Final version -- typos corrected)

Scientific paper

10.1142/S0129055X0500242X

We study the evolution of a quantum particle interacting with a random
potential in the low density limit (Boltzmann-Grad). The phase space density of
the quantum evolution defined through the Husimi function converges weakly to a
linear Boltzmann equation with collision kernel given by the full quantum
scattering cross section.

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