A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS
文献类型：期刊论文
| 作者 | Liu Chuangye |
| 刊名 | ACTA MATHEMATICA SCIENTIA
 |
| 出版日期 | 2010-05-01 |
| 卷号 | 30期号:3页码:841-856 |
| 关键词 | Gross-Pitaevskii equation Boson system density matrix BBGKY hierarchy |
| 产权排序 | 第一 |
| 英文摘要 | In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N(-1) V(a)(x(i) - x(j)) whereV(a)(x) = a(-2)V(x/a). It is well known that the Gross-Pitaevskii (GP) equation is a nonlinear Schrodinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of k-particle density matrices {circle times(k) u(t) k >= 1} solves the GP hierarchy. Denote by psi(N,t) the solution to the N-particle Schrodinger equation. Under the assumption that a = N(-epsilon) for 0 < epsilon < 3/4, we prove that asN -> infinity the limit points of the k-particle density matrices of ON,t, are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by integral V (x) dx. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 学科主题 | 数学物理 |
| 类目[WOS] | Mathematics |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | BOSE-GAS ; CONDENSATE ; EQUATION ; DYNAMICS ; SYSTEMS ; VORTEX |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000278171600017 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/2059]  |
| 专题 | 武汉物理与数学研究所_2011年以前论文发表（包括2011年） |
| 作者单位 | Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu Chuangye. A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS[J]. ACTA MATHEMATICA SCIENTIA,2010,30(3):841-856. |
| APA | Liu Chuangye.(2010).A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS.ACTA MATHEMATICA SCIENTIA,30(3),841-856. |
| MLA | Liu Chuangye."A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS".ACTA MATHEMATICA SCIENTIA 30.3(2010):841-856. |
入库方式： OAI收割
来源：武汉物理与数学研究所
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