Boltzmann distributed quantum steady states and their classical limit

Peter A. Markowich

doi:10.1515/form.1994.6.1

Boltzmann distributed quantum steady states and their classical limit

Peter A. Markowich^*

^*Corresponding author for this work

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

8 Scopus citations

Abstract

We prove existence and uniqueness of Boltzmann distributed quantum steady states of an electron ensemble which moves under the actions of the self-consistent Coulomb potential and of an external potential. The case of the particles confined to a three-dimensional bounded domain and the whole space case in R³ is analyzed. Also, we prove the existence of the classical limit. As the Planck constant tends to zero we obtain a Maxwellian eqilibrium solution of the Vlasov-Poisson problem.

Original language	English (US)
Pages (from-to)	1-34
Number of pages	34
Journal	Forum Mathematicum
Volume	6
Issue number	6
DOIs	https://doi.org/10.1515/form.1994.6.1
State	Published - 1994
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/form.1994.6.1

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abstract = "We prove existence and uniqueness of Boltzmann distributed quantum steady states of an electron ensemble which moves under the actions of the self-consistent Coulomb potential and of an external potential. The case of the particles confined to a three-dimensional bounded domain and the whole space case in R3 is analyzed. Also, we prove the existence of the classical limit. As the Planck constant tends to zero we obtain a Maxwellian eqilibrium solution of the Vlasov-Poisson problem.",

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AB - We prove existence and uniqueness of Boltzmann distributed quantum steady states of an electron ensemble which moves under the actions of the self-consistent Coulomb potential and of an external potential. The case of the particles confined to a three-dimensional bounded domain and the whole space case in R3 is analyzed. Also, we prove the existence of the classical limit. As the Planck constant tends to zero we obtain a Maxwellian eqilibrium solution of the Vlasov-Poisson problem.

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U2 - 10.1515/form.1994.6.1

DO - 10.1515/form.1994.6.1

M3 - Article

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SP - 1

EP - 34

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 6

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Boltzmann distributed quantum steady states and their classical limit

Abstract

ASJC Scopus subject areas

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