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Controllability of a quantum particle in a moving potential well

Abstract : We consider a nonrelativistic charged particle in a 1D moving potential well. This quantum system is subject to a control, which is the acceleration of the well. It is represented by a wave function solution of a Schrödinger equation, the position of the well together with its velocity. We prove the following controllability result for this bilinear control system: given an initial condition close enough to an eigenstate and a target close enough to another eigenstate, the wave function can be moved exactly from the first one to the second one in finite time. Moreover, we can control the position and the velocity of the well. Our proof uses moment theory, a Nash-Moser implicit function theorem, the return method and expansion to the second order.
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https://hal.archives-ouvertes.fr/hal-00825517
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Submitted on : Thursday, May 23, 2013 - 10:02:36 PM
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  • HAL Id : hal-00825517, version 1

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Karine Beauchard, J.M. Coron. Controllability of a quantum particle in a moving potential well. Journal of Functional Analysis, Elsevier, 2006, 232, pp.328-389. ⟨hal-00825517⟩

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