Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

Aitor Balmaseda, Davide Lonigro, Juan Manuel Pérez-Pardo

Published 2021-08-01Version 1

We investigate the controllability of an infinite-dimensional quantum system by modifying the boundary conditions instead of applying external fields. We analyse the existence of solutions of the Schr\"odinger equation for a time-dependent Hamiltonian with time-dependent domain, but constant form domain. A stability theorem for such systems, which improves known results, is proven. We study magnetic systems on Quantum Circuits, a higher-dimensional generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension. We consider a particular class of boundary conditions (quasi-$\delta$ boundary conditions) compatible with the graph structure. By applying the stability theorem, we prove that these systems are approximately controllable. Smooth control functions are allowed in this framework.