Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions
Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions
复制标题
DOI：
10.1016/j.chemphys.2007.10.037
复制
发表时间：
2008-05-23
期刊：
影响因子：
2.3
通讯作者：
Tanimura, Yoshitaka
中科院分区：
文献类型：
--
作者：
Ishizaki, Akihito;Tanimura, Yoshitaka
基于影响泛函理论，我们导出了与色噪声谐振池耦合的约化系统的非微扰运动方程，其中系统-谐振池耦合算符不一定与系统哈密顿量对易.所得的表达式与由二阶微扰近似导出的无时间卷积量子主方程一致，该主方程也等价于广义Redfield方程。出现这种一致性是因为，在非微扰情况下，弛豫算子来自高阶系统浴相互作用，可以作为影响算子纳入约化密度矩阵;而二阶相互作用仍然作为运动方程中的弛豫算子。虽然该方程描述了密度矩阵的精确动力学，但它不具有适当计算非线性响应函数的能力。这是因为方程不能描述记忆效应，记忆效应由于减少了对浴槽的描述而跨越了外部系统相互作用。为了说明这一点，我们已经计算了三阶二维（2D）光谱的两个能级系统从本方法和层次耦合方程的方法，可以处理量子系统浴相干由于其层次的形式主义。数值演示清楚地表明，在目前的形式主义作为快速退相配置文件的2D光谱的系统浴相关性的缺乏。(c)2007 Elsevier B. V.保留所有权利。
Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolution less quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra. (c) 2007 Elsevier B.V. All rights reserved.