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

Understand

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).