### 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) |
---|---|

Article number | 043302 |

Journal | Journal of Mathematical Physics |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - 2006 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Mathematical Physics*,

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

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 47, no. 4, 043302. https://doi.org/10.1063/1.2192968

}

TY - JOUR

T1 - On quantum extensions to classical spherical harmonics expansion/Fokker- Planck models

AU - Bourgade, J. P.

AU - Degond, P.

AU - Ḿhats, F.

AU - Ringhofer, Christian

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646390953&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646390953&partnerID=8YFLogxK

U2 - 10.1063/1.2192968

DO - 10.1063/1.2192968

M3 - Article

AN - SCOPUS:33646390953

VL - 47

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

M1 - 043302

ER -