Tarnowski W, Yusipov I, Laptyeva T, Denisov S, Chruściński D, Życzkowski K
Institute of Theoretical Physics, Uniwersytet Jagielloński, 30-348 Kraków, Poland.
Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia.
Phys Rev E. 2021 Sep;104(3-1):034118. doi: 10.1103/PhysRevE.104.034118.
Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.
连续时间马尔可夫演化在经典世界和量子世界中表现出明显的不同。我们考虑N维马尔可夫演化的随机生成器的系综，包括量子的和经典的，并评估它们的通用谱性质。然后我们展示了这两种类型的生成器如何通过超退相干联系起来。类似于将量子态转变为经典态的退相干机制，超退相干可用于将林德布拉德算符（量子演化的生成器）转变为柯尔莫哥洛夫算符（经典演化的生成器）。我们研究了经历超退相干的随机林德布拉德算符的谱，并证明在完全超退相干的极限下，所得算符表现出随机柯尔莫哥洛夫算符典型的谱密度。通过逐渐增加超退相干的强度，我们观察到了明显的量子到经典的转变。此外，我们定义了超相干化的逆过程，它是用于从经典态构造量子态的方案的推广。最后，我们通过复间距比研究相邻本征值之间的微观相关性，并观察到两种类型的随机生成器都出现了象征吉尼贝里普遍性类的马蹄形分布。值得注意的是，它在超退相干和超相干化过程中都得以保留。
