From completely positive maps to the quantum Markovian semigroup master equation
From completely positive maps to the quantum Markovian semigroup master equation
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DOI：
10.1016/s0301-0104(01)00330-5
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发表时间：
2001-06-15
期刊：
影响因子：
2.3
通讯作者：
Whaley, KB
中科院分区：
文献类型：
--
作者：
Lidar, DA;Bihary, Z;Whaley, KB
开放量子系统动力学理论的一个中心问题是导出一个严格的和计算上易处理的主方程的约化系统密度矩阵。一般来说，开放量子系统的演化是由一个完全正的线性映射描述的。我们展示了如何推导出一个完全积极的马尔可夫主方程（Lindblad方程）从这样的地图粗粒化的过程。我们提供了一个新的和明确的配方计算的主方程的系数，在弱耦合极限微扰理论。我们理论之外的唯一参数是粗粒度时间尺度。我们说明的方法，明确推导出的自旋玻色子模型的主方程。的结果进行评估，完全可解的情况下，纯退相，并发现一个很好的协议在时间尺度上的马尔可夫近似预计是有效的。该方法原则上可以扩展到包括非马尔可夫效应。(C)2001爱思唯尔科技有限公司。保留所有权利。
A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum system is described by a completely positive linear map. We show how to derive a completely positive Markovian master equation (the Lindblad equation) from such a map by a coarse-graining procedure. We provide a novel and explicit recipe for calculating the coefficients of the master equation, using perturbation theory in the weak-coupling limit. The only parameter external to our theory is the coarse-graining time-scale. We illustrate the method by explicitly deriving the master equation for the spin-boson model. The results are evaluated for the exactly solvable case of pure dephasing, and an excellent agreement is found within the time-scale where the Markovian approximation is expected to be valid. The method can be extended in principle to include non-Markovian effects. (C) 2001 Elsevier Science B.V. All rights reserved.