{
  "annotation_id": "8e8023cd-77cc-4b03-b630-86f9882c2de2",
  "date_created": "2026-03-02T18:02:23.220000Z",
  "date_modified": "2026-03-02T18:02:23.220000Z",
  "file_hash": "ede3da8b28916c6312c987b11d66810662f5c74d0b1ecfa42276d26657cdeb6f",
  "private": false,
  "record": {
    "abstract": "The time-dependent Schrodinger equation of a many particle spin system\nconsisting of an electron in a quantum dot interacting with the spins of the\nnuclei (N) in the dot due to hyperfine interaction is solved exactly for a\ngiven arbitrary initial state. The electron spin dynamics is then expressed in\nterms of the reduced density matrix of the composite system by computing the\nmarginal density matrix of the electron. This is accomplished by classifying\nstates of the system by the total spin of the coupled electron and nuclear\nsystem that commutes with the system Hamiltonian. These states are used in\nenumerating and finding the exact solution of the time-dependent Schrodinger\nequation. In each sector of the total spin, the problem reduces to solving a\nlinear simultaneous set of equations that are solved by matrix inversion. Such\nsolutions enable one to make a reliable approximate scheme for purposes of\nnumerical estimation of the various physical quantities. A methematical and\nphysical discussion of this procedure with the density matrix approach to this\nproblem is given here. To elucidate the procedure and its advantages, special\ncases of N=3,4 are given in some detail in an Appendix.",
    "arxiv_id": "quant-ph/0602092",
    "authors": [
      "A. K. Rajagopal"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el"
    ],
    "title": "Electron Spin Dynamics in a Quantum Dot due to Hyperfine Coupling with   Nuclei in the Dot - An Exact Analysis",
    "url": "https://arxiv.org/abs/quant-ph/0602092"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fa91a189-4cce-4c04-bf3e-b9ac91a01d47",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}