Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics
Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics
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DOI：
10.1063/1.3159671
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发表时间：
2009-07-14
影响因子：
4.4
通讯作者：
Burghardt, Irene
中科院分区：
文献类型：
--
作者：
Hughes, Keith H.;Christ, Clara D.;Burghardt, Irene
描述了一种非马尔可夫系统-环境动力学的方法，该方法基于耦合有效环境模式的层次结构的构造，该层次结构通过将该层次结构的最终成员耦合到马尔可夫浴池来终止。对于与子系统线性耦合的任意环境，离散化的谱密度被一系列包含越来越多的有效模式的近似谱密度所代替。本文用解析法构造的这一系列逼近式，保证了整个系统加浴池动态的精确表示，直到增加次数。类似于Mori理论，层级结构以连分式虚部的形式表现在近似谱密度中。对于层次结构在一、二、三级被截断的情况，描述了结果。结果表明，简化密度矩阵运动方程的计算结果与高维体系+浴波包计算结果吻合较好。在约化密度矩阵的计算中，系统和有效模系被显式地处理，并用Caldeira-Leggett方程及其推广到零温度来描述浴场对体系最后成员的影响。(C)2009年美国物理研究所。[DOI：10.1063/1.3159671]
An approach to non-Markovian system-environment dynamics is described which is based on the construction of a hierarchy of coupled effective environmental modes that is terminated by coupling the final member of the hierarchy to a Markovian bath. For an arbitrary environment, which is linearly coupled to the subsystem, the discretized spectral density is replaced by a series of approximate spectral densities involving an increasing number of effective modes. This series of approximants, which are constructed analytically in this paper, guarantees the accurate representation of the overall system-plus-bath dynamics up to increasing times. The hierarchical structure is manifested in the approximate spectral densities in the form of the imaginary part of a continued fraction similar to Mori theory. The results are described for cases where the hierarchy is truncated at the first-, second- ,and third-order level. It is demonstrated that the results generated from a reduced density matrix equation of motion and large dimensional system-plus-bath wavepacket calculations are in excellent agreement. For the reduced density matrix calculations, the system and hierarchy of effective modes are treated explicitly and the effects of the bath on the final member of the hierarchy are described by the Caldeira-Leggett equation and its generalization to zero temperature. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3159671]