Controllability of Schrödinger equations

Karine Beauchard[1]

  • [1] CMLA ENS Cachan 94230 Cachan

Séminaire Équations aux dérivées partielles (2005-2006)

  • Volume: 84, Issue: 7, page 1-18

Abstract

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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 time, by moving the potential well in a suitable way.The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].

How to cite

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Beauchard, Karine. "Controllability of Schrödinger equations." Séminaire Équations aux dérivées partielles 84.7 (2005-2006): 1-18. <http://eudml.org/doc/11144>.

@article{Beauchard2005-2006,
abstract = {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 time, by moving the potential well in a suitable way.The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].},
affiliation = {CMLA ENS Cachan 94230 Cachan},
author = {Beauchard, Karine},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
number = {7},
pages = {1-18},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Controllability of Schrödinger equations},
url = {http://eudml.org/doc/11144},
volume = {84},
year = {2005-2006},
}

TY - JOUR
AU - Beauchard, Karine
TI - Controllability of Schrödinger equations
JO - Séminaire Équations aux dérivées partielles
PY - 2005-2006
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 84
IS - 7
SP - 1
EP - 18
AB - 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 time, by moving the potential well in a suitable way.The proof uses moment theory, a Nash-Moser theorem, Coron’s return method and expansions to the second order.This article summarizes two works : [4] and a joint work with Jean-Michel Coron [5].
LA - eng
UR - http://eudml.org/doc/11144
ER -

References

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