Chebyshev hierarchical equations of motion for systems with arbitrary spectral densities and temperatures.
Chebyshev hierarchical equations of motion for systems with arbitrary spectral densities and temperatures.
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DOI：
10.1063/1.5100102
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发表时间：
2019-04
期刊：
影响因子：
--
通讯作者：
H. Rahman;U. Kleinekathöfer
中科院分区：
文献类型：
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作者：
H. Rahman;U. Kleinekathöfer
开放量子系统中的时间演化，如分子聚集体与热浴的接触，仍然是一个复杂而具有挑战性的问题。热噪声的影响可以用过多的格式来处理，其中一些格式以指数函数的加权和的形式分解相应的相关函数。一种这样的方案是基于分层运动方程(HEOM)，它只使用某些形式的浴关联函数来建立。在环境由复杂的光谱密度描述或处于非常低的温度的情况下，利用指数分解的方法变得非常低效。在这里，我们利用基于切比雪夫多项式和贝塞尔函数的浴场关联函数的另一种分解方案，推导出环境耦合中高达任意阶的HEOM方法。这些分层方程在结构上类似于流行的指数HEOM格式，但使用贝塞尔函数的导数来表示。对一个二能级系统进行了四阶微扰计算，并与零温量子欧姆和超欧姆噪声情况下的基准计算结果进行了比较。此外，还讨论了现有的切比雪夫方程的优点和不足。
The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here, we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a HEOM approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.