Classical limit for semirelativistic Hartree systems

Gonca L. Aki; Peter A. Markowich; Christof Sparber

doi:10.1063/1.3000059

Classical limit for semirelativistic Hartree systems

Gonca L. Aki, Peter A. Markowich, Christof Sparber

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

14 Scopus citations

Abstract

We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case.

Original language	English (US)
Article number	102110
Journal	Journal of Mathematical Physics
Volume	49
Issue number	10
DOIs	https://doi.org/10.1063/1.3000059
State	Published - 2008
Externally published	Yes

Bibliographical note

Funding Information:
This work has been supported by the KAUST Investigator Award and the Wolfson Research Merit Award (Royal Society) of P. Markowich. G. L. Aki acknowledges support by the DEASE project of the EU. C. Sparber has been supported by the APART grant of the Austrian Academy of Sciences (MEST-CT-2005-021122).

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3000059

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abstract = "We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case.",

author = "Aki, {Gonca L.} and Markowich, {Peter A.} and Christof Sparber",

note = "Funding Information: This work has been supported by the KAUST Investigator Award and the Wolfson Research Merit Award (Royal Society) of P. Markowich. G. L. Aki acknowledges support by the DEASE project of the EU. C. Sparber has been supported by the APART grant of the Austrian Academy of Sciences (MEST-CT-2005-021122).",

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AU - Sparber, Christof

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PY - 2008

Y1 - 2008

N2 - We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case.

AB - We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case.

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Classical limit for semirelativistic Hartree systems

Abstract

Bibliographical note

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