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

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

2001-08-29

arxiv.org/abs/math-ph/0108025v1

Physics

Mathematical Physics

Latex fil with 13 .eps files

Scientific paper

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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