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

Abstract

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with quasi-$\delta$ boundary conditions. This is a particular class of self-adjoint boundary conditions compatible with the graph structure. We prove that global approximate controllability can be achieved using two physically distinct protocols: either using the boundary conditions as controls, or using time-dependent magnetic fields. Both cases have time-dependent domains for the Hamiltonians.

The results on this article arise from splitting in two the original version. This contains the controllability results on higher dimensional versions of Quantum Graphs with magnetic laplacians. The results about existence and stability of the solutions of the non-autonomous Schrödinger equation appear in arXiv:2306.10203. This new version is the one accepted for publication

References in corpus (9)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Quantum wires with magnetic fluxes
• Convergence of resonances on thin branched quantum wave guides
• Quasienergy anholonomy and its application to adiabatic quantum state manipulation
• Physical interpretation of point-like interactions of one-dimensional Schrödinger operator
• Anomalous Hall conductivity and quantum friction
• On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
• A quantum hybrid with a thin antenna at the vertex of a wedge
• Quantum Control at the Boundary

Cited by in corpus (2)

• On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control
• Global approximate controllability of quantum systems by form perturbations and applications