Displaying similar documents to “Controllability of a quantum particle in a 1D variable domain”

Controllability of Schrödinger equations

Karine Beauchard (2005-2006)

Séminaire Équations aux dérivées partielles

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One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite...

Limitations on the control of Schrödinger equations

Reinhard Illner, Horst Lange, Holger Teismann (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control ( E ( t ) · x ) u is...

A theorem on the controllability of pertubated linear control systems

Ornella Naselli Ricceri (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In this Note, applying our recent Theorem 3.1 of [7], we prove that suitable perturbations of a completely controllable linear control system, do not affect the controllability of the system.

Null-controllability of some systems of parabolic type by one control force

Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.