Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting

Nader Masmoudi; Mohamed Lazhar Tayeb

doi:10.1016/j.matpur.2021.08.005

Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting

Nader Masmoudi, Mohamed Lazhar Tayeb

Research output: Contribution to journal › Article › peer-review

Abstract

An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.

Original language	English (US)
Pages (from-to)	42-70
Number of pages	29
Journal	Journal des Mathematiques Pures et Appliquees
Volume	158
DOIs	https://doi.org/10.1016/j.matpur.2021.08.005
State	Published - Feb 2022

Keywords

Boltzmann-Poisson
Entropy-dissipation
Fermi-Dirac statistics
Hydrodynamic limit
Quantum effects
Semiconductors

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1016/j.matpur.2021.08.005

Cite this

@article{90c6df77eca5425b9db18e3d4b5cadbc,

title = "Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting",

abstract = "An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.",

keywords = "Boltzmann-Poisson, Entropy-dissipation, Fermi-Dirac statistics, Hydrodynamic limit, Quantum effects, Semiconductors",

author = "Nader Masmoudi and Tayeb, {Mohamed Lazhar}",

note = "Funding Information: The work of N. M is supported by NSF grant DMS-1716466 and by Tamkeen under the NYU Abu Dhabi Research Institute grant of the center SITE. Publisher Copyright: {\textcopyright} 2021",

year = "2022",

month = feb,

doi = "10.1016/j.matpur.2021.08.005",

language = "English (US)",

volume = "158",

pages = "42--70",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

}

TY - JOUR

T1 - Macroscopic approximation of a Fermi-Dirac statistics

T2 - Unbounded velocity space setting

AU - Masmoudi, Nader

AU - Tayeb, Mohamed Lazhar

PY - 2022/2

Y1 - 2022/2

N2 - An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.

AB - An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.

KW - Boltzmann-Poisson

KW - Entropy-dissipation

KW - Fermi-Dirac statistics

KW - Hydrodynamic limit

KW - Quantum effects

KW - Semiconductors

UR - http://www.scopus.com/inward/record.url?scp=85113765731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85113765731&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2021.08.005

DO - 10.1016/j.matpur.2021.08.005

M3 - Article

AN - SCOPUS:85113765731

SN - 0021-7824

VL - 158

SP - 42

EP - 70

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Macroscopic approximation of a Fermi-Dirac statistics: Unbounded velocity space setting

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this