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Wigner measure and the semiclassical limit of Schrodinger-Poisson equations
Zhang, P
AbstractThe wave function {psi(epsilon)(t,x)} of single particle approximation, which is used in the study of quantum transportation in some semiconductive devices, satisfies Schrodinger-Poisson equations. It is well known that the Wigner transformation f(epsilon)(t,x,xi) of the corresponding wave function psi(epsilon)(t,x) satisfies the so-called Wigner Poisson equations. We pro e here that in any space dimension, with the initial data of the form rootrho(0)(epsilon)(x) exp(i/epsilon S-epsilon(x)) to the wave function, and before the formation of vortices, the Wigner measure f(t,x,xi), which is the weak limit of f(epsilon)(t,x,xi) as the normalized Planck constant epsilon approaches 0, satisfies Vlasov-Poisson equations, and the limits of the quantum density and momentum to the Schrodinger Poisson equations satisfy the pressureless Euler-Poisson equations.
KeywordSchrodinger-Poisson Euler-Poisson Vlasov-Poisson Wigner measure Wigner transformation pseudodifferential operator
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000180883500009
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Document Type期刊论文
Corresponding AuthorZhang, P
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Zhang, P. Wigner measure and the semiclassical limit of Schrodinger-Poisson equations[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2003,34(3):700-718.
APA Zhang, P.(2003).Wigner measure and the semiclassical limit of Schrodinger-Poisson equations.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,34(3),700-718.
MLA Zhang, P."Wigner measure and the semiclassical limit of Schrodinger-Poisson equations".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 34.3(2003):700-718.
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