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 Citations (Scopus)

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 - 2006

Fingerprint

Fokker-Planck
Spherical Harmonics
spherical harmonics
expansion
operators
hierarchies
Wigner Equation
H-theorem
theorems
Scattering Operator
Model
Phonon
First-principles
collisions
approximation
scattering
Collision
Electron
electrons
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

On quantum extensions to classical spherical harmonics expansion/Fokker- Planck models. / Bourgade, J. P.; Degond, P.; Ḿhats, F.; Ringhofer, Christian.

In: Journal of Mathematical Physics, Vol. 47, No. 4, 043302, 2006.

Research output: Contribution to journalArticle

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