Laszlo Erdos
Linear Boltzmann equation as the long time dynamics of an electron
weakly coupled to a phonon field
(349K, Latex with 13 .eps files)
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.