Displaying similar documents to “Controllability of the discrete-spectrum Schrödinger equation driven by an external field”

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...

Controllability of a quantum particle in a 1D variable domain

Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function φ of the particle and the control is the length l ( t ) of the potential well. We prove the following controllability result : given φ 0 close enough to an eigenstate corresponding to the length l = 1 and φ f close enough to another eigenstate corresponding to the length l = 1 , there exists a continuous function l : [ 0 , T ] → ℝ + * with T > 0 , such that l ( 0 ) = 1 and l ( T ) = 1 ,...

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...