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Controllability of a 2D quantum particle in a time-varying disc with radial data

Abstract : In this article we consider a 2-D quantum particle confined 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 control variable. We prove that the resulting system is locally controllable around some radial trajectories which are linear combinations of the first three radial eigenfunc-tions 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.
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https://hal.archives-ouvertes.fr/hal-01405624
Contributor : Moyano Iván Connect in order to contact the contributor
Submitted on : Wednesday, November 30, 2016 - 11:10:12 AM
Last modification on : Thursday, April 29, 2021 - 6:04:02 PM
Long-term archiving on: : Monday, March 27, 2017 - 8:04:14 AM

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  • HAL Id : hal-01405624, version 1
  • ARXIV : 1611.10192

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Iván Moyano. Controllability of a 2D quantum particle in a time-varying disc with radial data. 2016. ⟨hal-01405624⟩

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