Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China.
Center for Advanced Optoelectronic Functional Materials Research, and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China.
Phys Rev E. 2017 Jan;95(1-1):012156. doi: 10.1103/PhysRevE.95.012156. Epub 2017 Jan 30.
The Kubo formula is an equation that expresses the linear response of an observable due to a time-dependent perturbation. It has been extended from closed systems to open systems in recent years under the Markovian approximation, but is barely explored for open systems in non-Markovian regimes. In this paper, we derive a formula for the linear response of an open system to a time-independent external field. This response formula is available for both Markovian and non-Markovian dynamics depending on parameters in the spectral density of the environment. As an illustration of the theory, the Hall conductance of a two-band system subjected to environments is derived and discussed. With the tight-binding model, we point out the Hall conductance changes from Markovian to non-Markovian dynamics by modulating the spectral density of the environment. Our results suggest a way to the controlling of the system response, which has potential applications for quantum statistical mechanics and condensed matter physics.
久保公式是一个用来表达由于时变微扰而导致可观测线性响应的方程。近年来，在马尔科夫近似下，它已经从封闭系统扩展到开放系统，但在非马尔科夫环境下，对于开放系统的研究几乎没有涉及。在本文中，我们推导出了一个开放系统对时不变外场的线性响应公式。该响应公式适用于马尔科夫和非马尔科夫动力学，具体取决于环境谱密度中的参数。作为理论的一个说明，我们推导出了一个双能带系统在环境作用下的霍尔电导，并进行了讨论。通过紧束缚模型，我们指出通过调制环境的谱密度，霍尔电导可以从马尔科夫动力学变为非马尔科夫动力学。我们的结果为控制系统响应提供了一种方法，这在量子统计力学和凝聚态物理中有潜在的应用。
