Control of the Schrödinger equation by slow deformations of the domain
Alessandro Duca
Université de Lorraine, CNRS, Nancy, FranceRomain Joly
Université Grenoble Alpes, CNRS, Institut Fourier, Grenoble, FranceDmitry Turaev
Imperial College London, UK; Higher School of Economics - Nizhny Novgorod, Russia
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 by 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 Anal. Non Linéaire 41 (2024), no. 3, pp. 511–553
DOI 10.4171/AIHPC/86