✦ LIBER ✦

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

✍ Scribed by László Erdős; Horng-Tzer Yau

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 392 KB
Volume: 53
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(200006)53:6<667::aid-cpa1>3.0.co;2-5

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✦ Synopsis

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.