On quantum extensions to classical spherical harmonics expansion/Fokker- Planck models

J. P. Bourgade, P. Degond, F. Ḿhats, Christian Ringhofer

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

By following a strategy introduced in previous works, quantum extensions of the classical electron-phonon scattering operator are deduced from first principles. These quantum collision operators satisfy a quantum H-theorem and relax towards quantum equilibria. Then, under an assumption of dominant elastic interactions, a hierarchy of quantum spherical harmonic expansion (SHE) models is derived by a diffusive approximation of collisional Wigner equations. These models are proven entropic and their expansions into powers of the reduced Planck constant are calculated, leading to 2 corrections for the classical SHE model.

Original languageEnglish (US)
Article number043302
JournalJournal of Mathematical Physics
Volume47
Issue number4
DOIs
StatePublished - May 15 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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