Random generators of Markovian evolution: A quantum-classical transition by superdecoherence,Physical Review E

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Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-14 , DOI: 10.1103/physreve.104.034118
W Tarnowski ₁ , I Yusipov ₂ , T Laptyeva ₂ , S Denisov ₃ , D Chruściński ₄ , K Życzkowski _{1,

5}

Affiliation

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.

中文翻译：

马尔可夫进化的随机发生器：超退相干的量子经典转变

连续时间马尔可夫进化在经典世界和量子世界中似乎明显不同。我们考虑随机生成器的集合

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维马尔可夫演化、量子和经典演化，并评估它们的通用光谱特性。然后我们展示了这两种类型的发生器如何通过超退相干相关联。与将量子态转换为经典态的退相干机制类似，超退相干可用于将 Lindblad 算子（量子演化发生器）转换为 Kolmogorov 算符（经典演化发生器）。我们检查了经历超退相干的随机 Lindblad 算子的频谱，并证明，在完全超退相干的限制下，得到的算子表现出随机 Kolmogorov 算子的典型频谱密度。通过逐渐增加超退相干的强度，我们观察到从量子到经典的急剧转变。此外，我们定义了一个超相干化的逆过程，它是用于从经典状态构建量子状态的方案的概括。最后，我们通过复杂的间距比研究相邻特征值之间的微观相关性，并观察两种类型的随机生成器的马蹄形分布，这是 Ginibre 普遍性类的象征。值得注意的是，它同时经受住了超消相干和超相干化。

更新日期：2021-09-15

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