On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities

doi:10.1016/j.jde.2022.11.021

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	On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities
	Coron, Jean-Michel 1; Xiang, Shengquan 2; Zhang, Ping 3,4
	2023-02-05
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	345 页码:1-44
摘要	In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schrodinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of the physical observables via the Agrachev-Sarychev method. Then we conclude the proof through techniques of semiclassical approximation of the nonlinear Schrodinger equation. (c) 2022 Elsevier Inc. All rights reserved.
关键词	Semiclassical Schr?dinger equation Quantum density Quantum momentum Controllability Semiclassical limit
DOI	10.1016/j.jde.2022.11.021
收录类别	SCI
语种	英语
资助项目	Chair of Partial Differential Equations at EPFL ; K. C. Wong Education Foundation ; NSF of China[12288201] ; NSF of China[11731007] ; NSF of China[12031006]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000897817400001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60504
专题	中国科学院数学与系统科学研究院
通讯作者	Xiang, Shengquan
作者单位	1.Sorbonne Univ, Univ Paris Diderot SPC, Equipe CAGE, CNRS,INRIA,Lab Jacques Louis Lions LJLL, F-75005 Paris, France 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Coron, Jean-Michel,Xiang, Shengquan,Zhang, Ping. On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2023,345:1-44.
APA	Coron, Jean-Michel,Xiang, Shengquan,&Zhang, Ping.(2023).On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities.JOURNAL OF DIFFERENTIAL EQUATIONS,345,1-44.
MLA	Coron, Jean-Michel,et al."On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities".JOURNAL OF DIFFERENTIAL EQUATIONS 345(2023):1-44.