Alessandro Duca - Schrödinger equation on moving domains: well-posedness, quasi-adiabatic control, and implementation

Nous aurons l'occasion d'écouter une présentation d'Alessandro Duca (Institut Elie Cartan de Lorraine) intitulée Schrödinger equation on moving domains: well-posedness, quasi-adiabatic control, and implementation, le 27 novembre 2025 à l'ENSTA Paris en Amphi 2234. 

Résumé :
We consider a Schrödinger equation on a time-varying domain and discuss how to define solutions of such an equation, which is naturally defined on a time-dependent Hilbert space. For this purpose, we propose a specific family of unitary transformations, which we use to rewrite the Schr¨odinger equation on a fixed domain. By exploiting the Hamiltonian structure of this equivalent equation, we ensure the well-posedness of the initial problem endowed with suitable boundary conditions. Afterwards, we describe how to approximately control the equation through suitable deformations of the domain. We begin by presenting an abstract result on controllability, and then we examine explicit deformations, discussing their practical implementability.