Phenomenological memory-kernel master equations and time-dependent Markovian processes
Phenomenological memory-kernel master equations and time-dependent Markovian processes
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DOI：
10.1103/physreva.81.062120
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发表时间：
2010-03
影响因子：
2.9
通讯作者：
L. Mazzola;Elsi-Marie Laine;H. Breuer;Sabrina Maniscalco;J. Piilo
中科院分区：
文献类型：
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作者：
L. Mazzola;Elsi-Marie Laine;H. Breuer;Sabrina Maniscalco;J. Piilo
具有记忆核的唯象主方程是否总是描述以信息反向流动为特征的非马尔可夫量子动力学？对系统过去状态的整合是非马尔可夫性的明确无误的标志吗？我们通过一个反例表明，情况并非总是如此。我们考虑两个常用的唯象积分-微分主方程描述的动力学自旋1/2的热浴。通过使用最近引入的度量来量化非马尔可夫性[Breuer等人，物理修订信函103，210401（2009）]我们证明，只要方程保持其物理意义，非马尔可夫行为的关键特征不会出现在所考虑的内存内核主方程中。也就是说，没有从环境到开放系统的反向信息流。因此，在记忆核上的积分总是导致非马尔可夫动力学的假设，原来是脆弱的现象学近似。相反，所考虑的唯象方程能够描述与时间相关的马尔可夫过程的系统与时间相关的单向信息流的水库。
Do phenomenological master equations with a memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [Breuer et al., Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and unidirectional information flow from the system to the reservoir associated with time-dependent Markovian processes.