Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
arXiv:2108.00495 · doi:10.1088/1751-8121/ace505
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- 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.
arXiv commentThe 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
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