Random generators of Markovian evolution: A quantum-classical transition by superdecoherence

TL;DR

This paper investigates the spectral properties of random Markovian generators in quantum and classical systems, demonstrating a transition via superdecoherence and revealing universal spectral features and correlations.

Contribution

It introduces superdecoherence as a mechanism to connect quantum and classical Markovian generators and analyzes their spectral properties and universality classes.

Findings

Superdecoherence transforms quantum Lindblad operators into classical Kolmogorov operators.

Spectral density of operators approaches that of classical generators under superdecoherence.

The complex spacing ratios exhibit Ginibre universality, persisting through the quantum-classical transition.

Abstract

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 neighbouring eigenvalues through the complex spacing ratios and observe the horse-shoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives superdecoherence and supercoherification.