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Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field

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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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Authors and Affiliations

  1. School of Mathematics, GeorgiaTech, Atlanta, Georgia, 30332

    László Erdős

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  1. László Erdős
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Erdős, L. Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field. Journal of Statistical Physics 107, 1043–1127 (2002). https://doi.org/10.1023/A:1015157624384

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  • DOI: https://doi.org/10.1023/A:1015157624384

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