Global exact controllability of a 1D Schrödinger equations with a polarizability term

2013/09/26 by Morgan Morancey, Morancey, Morgan, Vahagn Nersesyan +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Laser-Matter Interactions and Applications #Quantum chaos and dynamical systems #math.AP #math.OC

paper · pdf · doi:10.48550/arxiv.1309.6959

Contains an abridged French version

arxiv created 2013/09/26 · arxiv updated 2013/09/27

Abstract

We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with respect to the control), we prove global exact controllability in a suitable space for arbitrary potential and arbitrary dipole moment. This term is relevant both from the mathematical and physical points of view. The proof uses tools from the bilinear setting and a perturbation argument.

Related

• Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms
• Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schrödinger equations
• Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control
• Controllability of bilinear quantum systems in explicit times via\n explicit control fields
• Global exact controllability in infinite time of Schrödinger equation