Control of the Schrödinger equation by slow deformations of the domain

  • Alessandro Duca

    Université de Lorraine, CNRS, Nancy, France
  • Romain Joly

    Université Grenoble Alpes, CNRS, Institut Fourier, Grenoble, France
  • Dmitry Turaev

    Imperial College London, UK; Higher School of Economics - Nizhny Novgorod, Russia
Control of the Schrödinger equation by slow deformations of the domain cover

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Abstract

The aim of this work is to study the controllability of the Schrödinger equation on with Dirichlet boundary conditions, where is a time-varying domain. We prove the global approximate controllability of the equation in , via an adiabatic deformation () such that . This control is strongly based on the Hamiltonian structure of the equation provided byby Duca and Joly [Ann. Henri Poincaré 22 (2021), 2029–2063], which enables the use of adiabatic motions.We also discuss several explicit interesting controls that we perform in the specific framework of rectangular domains.

Cite this article

Alessandro Duca, Romain Joly, Dmitry Turaev, Control of the Schrödinger equation by slow deformations of the domain. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2023), published online first

DOI 10.4171/AIHPC/86