Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan.
J Chem Phys. 2011 Mar 28;134(12):124112. doi: 10.1063/1.3570581.
An extremely useful evolution equation that allows systematically calculating the two-time correlation functions (CF's) of system operators for non-Markovian open (dissipative) quantum systems is derived. The derivation is based on perturbative quantum master equation approach, so non-Markovian open quantum system models that are not exactly solvable can use our derived evolution equation to easily obtain their two-time CF's of system operators, valid to second order in the system-environment interaction. Since the form and nature of the Hamiltonian are not specified in our derived evolution equation, our evolution equation is applicable for bosonic and/or fermionic environments and can be applied to a wide range of system-environment models with any factorized (separable) system-environment initial states (pure or mixed). When applied to a general model of a system coupled to a finite-temperature bosonic environment with a system coupling operator L in the system-environment interaction Hamiltonian, the resultant evolution equation is valid for both L = L(†) and L ≠ L(†) cases, in contrast to those evolution equations valid only for L = L(†) case in the literature. The derived equation that generalizes the quantum regression theorem (QRT) to the non-Markovian case will have broad applications in many different branches of physics. We then give conditions on which the QRT holds in the weak system-environment coupling case and apply the derived evolution equation to a problem of a two-level system (atom) coupled to the finite-temperature bosonic environment (electromagnetic fields) with L ≠ L(†).
推导出了一个非常有用的演化方程，该方程可以系统地计算非马尔可夫开（耗散）量子系统的系统算子的两时间相关函数（CF）。该推导基于微扰量子主方程方法，因此，对于那些无法精确求解的非马尔可夫开量子系统模型，可以使用我们推导出的演化方程来轻松获得其系统算子的两时间 CF，其有效性可以达到系统-环境相互作用的二阶。由于我们推导出的演化方程中没有指定哈密顿量的形式和性质，因此我们的演化方程适用于玻色子和/或费米子环境，并且可以应用于具有任何因子化（可分离）系统-环境初始状态（纯态或混合态）的广泛的系统-环境模型。当应用于一个系统与有限温度玻色子环境耦合的一般模型时，系统耦合算符 L 处于系统-环境相互作用哈密顿量中，所得演化方程在 L = L(†)和 L ≠ L(†)两种情况下均有效，这与文献中仅在 L = L(†)情况下有效的那些演化方程形成对比。将量子回归定理（QRT）推广到非马尔可夫情况的导出方程将在物理学的许多不同分支中具有广泛的应用。然后，我们给出了在弱系统-环境耦合情况下 QRT 成立的条件，并将推导出的演化方程应用于一个两能级系统（原子）与有限温度玻色子环境（电磁场）耦合的问题，其中 L ≠ L(†)。
