Stochastic limit approximation for rapidly decaying systems

Details Stochastic limit approximation for rapidly decaying systems Stochastic limit approximation for rapidly decaying systems

2000-07-04

arxiv.org/abs/quant-ph/0007007v2

Phys. Rev. A 63 (2001) 022103

Physics

Quantum Physics

REVTeX, 6 pages; To be published in Phys. Rev. A 63 (Feb. 2000)

Scientific paper

10.1103/PhysRevA.63.022103

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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