A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS

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	A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS
	Liu Chuangye
刊名	ACTA MATHEMATICA SCIENTIA
	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.
学科主题	数学物理
WOS标题词	Science & Technology ; Physical Sciences
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
内容类型	期刊论文
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.