| Wigner measure and the semiclassical limit of Schrodinger-Poisson equations | |
Zhang, P
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| 2003-01-28 | |
| Source Publication | SIAM JOURNAL ON MATHEMATICAL ANALYSIS
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| 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. |
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