期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:455
Controllability of a 2D quantum particle in a time-varying disc with radial data
Article
Moyano, Ivan1,2 
[1] Mines Paris Tech, Ctr Robot CAOR, 60 Bld St Michel, F-75282 Paris, France
[2] UPMC, Lab Jacques Louis Lions, 4 Pl Jussieu, F-75252 Paris, France
关键词: Schrodinger equation;    Control theory;    Bessel functions;    Moment problem;    Riesz basis;    Nonharmonic Fourier series;   
DOI  :  10.1016/j.jmaa.2017.05.002
来源: Elsevier
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【 摘 要 】

In this article we consider a 2-D quantum particle confined in a disc whose radius can be deformed continuously in time. We study the problem of controllability of such a quantum particle via deformations of the initial disc, i.e., when we set the time-dependent radius of the disc to be the control variable. We prove that the resulting system is locally controllable around some radial trajectories which are linear combinations of the first three radial eigenfunctions of the Laplacian in the unit disc with Dirichlet boundary conditions. We prove this result, thanks to the linearisation principle, by studying the linearised system, which leads to a moment problem that can be solved using some results from Nonharmonic Fourier series. In particular, we have to deal with fine properties of Bessel functions. (C) 2017 Elsevier Inc. All rights reserved.

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