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

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This study reveals how superdecoherence bridges quantum and classical Markovian evolution. It demonstrates a quantum-to-classical transition and a reversible supercoherification process, with spectral properties surviving transformations.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Dynamical systems

Background:

  • Markovian evolution differs significantly between classical and quantum systems.
  • Understanding spectral properties of random generators is key to characterizing these systems.
  • Decoherence transforms quantum states into classical ones.

Purpose of the Study:

  • To investigate universal spectral properties of random generators for N-dimensional Markovian evolution, both quantum and classical.
  • To establish a relationship between quantum and classical generators using superdecoherence.
  • To explore the quantum-to-classical transition and its reversibility via supercoherification.

Main Methods:

  • Ensemble averaging of random Lindblad (quantum) and Kolmogorov (classical) operators.
  • Analysis of spectral densities and eigenvalue correlations.
  • Introduction and application of the superdecoherence and supercoherification procedures.

Main Results:

  • Superdecoherence transforms Lindblad operators into Kolmogorov operators, inducing a sharp quantum-to-classical transition.
  • The inverse procedure, supercoherification, is defined and shown to be a generalization of quantum state construction.
  • Microscopic eigenvalue correlations, characterized by the horseshoe distribution, are robust to both superdecoherence and supercoherification.

Conclusions:

  • Superdecoherence provides a mechanism to unify the description of quantum and classical Markovian dynamics.
  • The observed quantum-to-classical transition is sharp and reversible.
  • The Ginibre universality class, indicated by eigenvalue correlations, is a common feature for both quantum and classical random generators.