dorsal/arxiv
View SchemaElectron Spin Dynamics in a Quantum Dot due to Hyperfine Coupling with Nuclei in the Dot - An Exact Analysis
| Authors | A. K. Rajagopal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602092 |
| URL | https://arxiv.org/abs/quant-ph/0602092 |
Abstract
The time-dependent Schrodinger equation of a many particle spin system consisting of an electron in a quantum dot interacting with the spins of the nuclei (N) in the dot due to hyperfine interaction is solved exactly for a given arbitrary initial state. The electron spin dynamics is then expressed in terms of the reduced density matrix of the composite system by computing the marginal density matrix of the electron. This is accomplished by classifying states of the system by the total spin of the coupled electron and nuclear system that commutes with the system Hamiltonian. These states are used in enumerating and finding the exact solution of the time-dependent Schrodinger equation. In each sector of the total spin, the problem reduces to solving a linear simultaneous set of equations that are solved by matrix inversion. Such solutions enable one to make a reliable approximate scheme for purposes of numerical estimation of the various physical quantities. A methematical and physical discussion of this procedure with the density matrix approach to this problem is given here. To elucidate the procedure and its advantages, special cases of N=3,4 are given in some detail in an Appendix.
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"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"
},
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