### 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 language | English (US) |
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Article number | 043302 |

Journal | Journal of Mathematical Physics |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - May 15 2006 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Bourgade, J. P., Degond, P., Ḿhats, F., & Ringhofer, C. (2006). On quantum extensions to classical spherical harmonics expansion/Fokker- Planck models.

*Journal of Mathematical Physics*,*47*(4), [043302]. https://doi.org/10.1063/1.2192968