{
  "id": "2108.00495",
  "version": "v1",
  "published": "2021-08-01T17:10:52.000Z",
  "updated": "2021-08-01T17:10:52.000Z",
  "title": "Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions",
  "authors": [
    "Aitor Balmaseda",
    "Davide Lonigro",
    "Juan Manuel Pérez-Pardo"
  ],
  "comment": "37 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OC",
    "quant-ph"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-01T17:10:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q93",
      "81Q35",
      "35Q41",
      "35J10"
    ],
    "keywords": [
      "boundary conditions",
      "magnetic potentials",
      "quantum controllability",
      "graph-like manifolds",
      "stability theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}