dorsal/arxiv
View SchemaStochastic limit approximation for rapidly decaying systems
| Authors | Gen Kimura, Kazuya Yuasa, Kentaro Imafuku |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0007007 |
| URL | https://arxiv.org/abs/quant-ph/0007007 |
| DOI | 10.1103/PhysRevA.63.022103 |
| Journal | Phys. Rev. A 63 (2001) 022103 |
Abstract
The stochastic limit approximation method for ``rapid'' decay is presented, where the damping rate \gamma is comparable to the system frequency \Omega, i.e., \gamma \sim \Omega, whereas the usual stochastic limit approximation is applied only to the weak damping situation \gamma << \Omega. The key formulas for rapid decay are very similar to those for weak damping, but the dynamics is quite different. From a microscopic Hamiltonian, the spin-boson model, a Bloch equation containing two independent time scales is derived. This is a useful method to extract the minimal dissipative dynamics at high temperature kT >> \hbar\Omega and the master equations obtained are of the Lindblad form even for the Caldeira-Leggett model. The validity of the method is confirmed by comparing the master equation derived through this method with the exact one.
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"abstract": "The stochastic limit approximation method for ``rapid\u0027\u0027 decay is presented,\nwhere the damping rate \\gamma is comparable to the system frequency \\Omega,\ni.e., \\gamma \\sim \\Omega, whereas the usual stochastic limit approximation is\napplied only to the weak damping situation \\gamma \u003c\u003c \\Omega. The key formulas\nfor rapid decay are very similar to those for weak damping, but the dynamics is\nquite different. From a microscopic Hamiltonian, the spin-boson model, a Bloch\nequation containing two independent time scales is derived. This is a useful\nmethod to extract the minimal dissipative dynamics at high temperature kT \u003e\u003e\n\\hbar\\Omega and the master equations obtained are of the Lindblad form even for\nthe Caldeira-Leggett model. The validity of the method is confirmed by\ncomparing the master equation derived through this method with the exact one.",
"arxiv_id": "quant-ph/0007007",
"authors": [
"Gen Kimura",
"Kazuya Yuasa",
"Kentaro Imafuku"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.63.022103",
"journal_ref": "Phys. Rev. A 63 (2001) 022103",
"title": "Stochastic limit approximation for rapidly decaying systems",
"url": "https://arxiv.org/abs/quant-ph/0007007"
},
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