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

	On the global approximate controllability in small time of semiclassical 1-D Schrodinger equations between two states with positive quantum densities
	Coron, Jean-Michel 2; Xiang, Shengquan 3; Zhang, Ping 1,4
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2023-02-05
卷号	345 页码:1-44
关键词	Semiclassical Schr?dinger equation Quantum density Quantum momentum Controllability Semiclassical limit
ISSN号	0022-0396
DOI	10.1016/j.jde.2022.11.021
英文摘要	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.
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
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000897817400001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60503]
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.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China 2.Sorbonne Univ, Univ Paris Diderot SPC, Equipe CAGE, CNRS,INRIA,Lab Jacques Louis Lions LJLL, F-75005 Paris, France 3.Peking Univ, Sch Math Sci, Beijing 100871, 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.