快速衰减系统的随机极限逼近
Stochastic limit approximation for rapidly decaying systems
摘要：
本文提出了“快”衰减的随机极限近似方法，其中阻尼率γ与系统频率Ω相当，即，γ \sim Ω，而通常的随机极限近似仅适用于弱阻尼情况γ<< Ω。快速衰减的关键公式与弱阻尼的公式非常相似，但动力学完全不同。从微观哈密顿量--自旋玻色子模型出发，导出了包含两个独立时标的布洛赫方程。这是一种提取高温kT >> \hbar Ω时最小耗散动力学的有效方法，即使对于Caldeira-Leggett模型，所得到的主方程也是Lindblad形式的。通过将该方法导出的主方程与精确主方程进行比较，验证了该方法的有效性。
英文摘要：
The stochastic limit approximation method for ``rapid'' decay is presented, where the damping rate γis comparable to the system frequency Ω, i.e., γ\sim 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 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 >> \hbarΩand 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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