Stochastic limit approximation for rapidly decaying systems
Abstract
The stochastic limit approximation method for ``rapid'' decay is presented, where the damping rate γ is comparable to the system frequency Ω, i.e., γ~Ω, whereas the usual stochastic limit approximation is applied only to the weak damping situation γ<<Ω. The key formulas for rapid decay are very similar to those for weak damping, but the dynamics are quite different. From a microscopic Hamiltonian, the spinboson 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 k_{B}T>>ħΩ and the master equations obtained are of the Lindblad form unlike that of Caldeira and Leggett. The validity of the method is confirmed by comparing the master equation derived through this method with the exact one.
 Publication:

Physical Review A
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevA.63.022103
 arXiv:
 arXiv:quantph/0007007
 Bibcode:
 2001PhRvA..63b2103K
 Keywords:

 03.65.Sq;
 05.30.d;
 42.50.Lc;
 02.50.r;
 Semiclassical theories and applications;
 Quantum statistical mechanics;
 Quantum fluctuations quantum noise and quantum jumps;
 Probability theory stochastic processes and statistics;
 Quantum Physics
 EPrint:
 REVTeX, 6 pages