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Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
Author(s) -
Erdős László,
Yau HorngTzer
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200006)53:6<667::aid-cpa1>3.0.co;2-5
Subject(s) - boltzmann equation , mathematics , limit (mathematics) , wigner distribution function , mathematical analysis , gaussian , schrödinger equation , coupling (piping) , stochastic differential equation , statistical physics , mathematical physics , quantum , quantum mechanics , physics , mechanical engineering , engineering
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. © 2000 John Wiley & Sons, Inc.