Boltzmann distributed quantum steady states and their classical limit

Peter A. Markowich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)1-34
Number of pages34
JournalForum Mathematicum
Issue number6
StatePublished - 1994
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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