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Approximate controllability of the Schr\"{o}dinger Equation with a polarizability term in higher Sobolev norms

Authors
  • Boussaid, Nabile
  • Caponigro, Marco
  • Chambrion, Thomas
Type
Preprint
Publication Date
Jun 15, 2014
Submission Date
Jun 15, 2014
Identifiers
arXiv ID: 1406.3846
Source
arXiv
License
Yellow
External links

Abstract

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field induced dipole moment. Sufficient conditions for approximate controllability are given. For transfers between eigenstates of the free Hamiltonian, the control laws are explicitly given. The results apply also for unbounded or non-regular potentials.

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