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

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2023-07-19
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IOP Publishing Limited
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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.
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Higher Dimensional Quantum Graphs, Quantum Control In Infinite Dimensions, Quantum Graphs, Self-Adjoint Boundary Conditions, Time Dependent Boundary Conditions, Time Dependent Magnetic Laplacians
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Balmaseda, A., Lonigro, D., & Pérez-Pardo, J. M. (2023). Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions. Journal of Physics A: Mathematical and Theoretical, 56(32), 325201.