Wigner measure and the semiclassical limit of Schrodinger-Poisson equations | |
Zhang, P | |
2003-01-28 | |
Source Publication | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
ISSN | 0036-1410 |
Volume | 34Issue:3Pages:700-718 |
Abstract | The 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. |
Keyword | Schrodinger-Poisson Euler-Poisson Vlasov-Poisson Wigner measure Wigner transformation pseudodifferential operator |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000180883500009 |
Publisher | SIAM PUBLICATIONS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/18251 |
Collection | 数学所 |
Affiliation | Chinese 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. |
Files in This Item: | ||||||
There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment