Breakdown of Markovianity by interactions in stroboscopic Floquet-Lindblad dynamics under high-frequency drive
Breakdown of Markovianity by interactions in stroboscopic Floquet-Lindblad dynamics under high-frequency drive
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DOI：
10.1103/physreva.103.l020202
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发表时间：
2021-02
影响因子：
2.9
通讯作者：
Kaoru Mizuta;K. Takasan;N. Kawakami
中科院分区：
文献类型：
--
作者：
Kaoru Mizuta;K. Takasan;N. Kawakami
Floquet-Magnus（FM）展开理论是研究高频驱动下周期驱动（Floquet）系统的有力工具。在封闭系统中，它规定了它们的频闪动力学下的时间周期的哈密顿量是很好地捕获的FM展开，这给出了一个静态的有效哈密顿量。另一方面，在由时间周期Liouvillian驱动的耗散系统中，FM展开是否给出描述连续时间马尔可夫动力学的静态Liouvillian仍然是一个重要而重要的问题，我们称之为FM展开的“Liouvillian”。我们回答这个问题的通用系统与当地的相互作用。我们发现，虽然非相互作用系统可以打破或保存Liouvillianity的FM扩展，通用的少体和多体相互作用系统打破它在任何有限的驱动器，这基本上是由传播的相互作用通过高阶项的FM扩展。Liouvillianity破缺意味着高频区域的马尔可夫耗散Floquet系统没有静态（马尔可夫）对应物，给出了涌现非马尔可夫性的签名。我们的理论提供了一个有用的洞察力在寻求独特的现象在耗散Floquet系统。
Floquet-Magnus (FM) expansion theory is a powerful tool in periodically driven (Floquet) systems under high-frequency drives. In closed systems, it dictates that their stroboscopic dynamics under a time-periodic Hamiltonian is well captured by the FM expansion, which gives a static effective Hamiltonian. On the other hand, in dissipative systems driven by a time-periodic Liouvillian, it remains an important and nontrivial problem whether the FM expansion gives a static Liouvillian describing continuous-time Markovian dynamics, which we refer to as the ``Liouvillianity'' of the FM expansion. We answer this question for generic systems with local interactions. We find that while noninteracting systems can either break or preserve Liouvillianity of the FM expansion, generic few-body and many-body interacting systems break it under any finite drive, which is essentially caused by propagation of interactions via higher-order terms of the FM expansion. Liouvillianity breaking implies that Markovian dissipative Floquet systems in the high-frequency regimes do not have static (Markovian) counterparts, giving a signature of emergent non-Markovianity. Our theory provides a useful insight in the quest for unique phenomena in dissipative Floquet systems.