{
  "id": "1701.02679",
  "version": "v1",
  "published": "2017-01-10T16:46:54.000Z",
  "updated": "2017-01-10T16:46:54.000Z",
  "title": "Investigation of optimal control problems governed by a time-dependent Kohn-Sham model",
  "authors": [
    "Martin Sprengel",
    "Gabriele Ciaramella",
    "Alfio Borzì"
  ],
  "categories": [
    "math.OC",
    "quant-ph"
  ],
  "abstract": "Many application models in quantum physics and chemistry require to control multi-electron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schr\\\"{o}dinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-10T16:46:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problems",
      "time-dependent kohn-sham model",
      "investigation",
      "time-dependent density functional theory",
      "kohn-sham tddft optimality systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}