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Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field

Laszlo Erdos
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Abstract

We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes.

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Laszlo Erdos. 2001-08-29. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. https://doi.org/10.1023/a%3A1015157624384

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