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Random-matrix theory for the Lindblad master equation.

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  • 1Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, P.O. Box 60 12 03, 14412 Potsdam, Germany.

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Random-matrix theory reveals spectral properties of the Lindblad superoperator, governing open quantum systems. This analysis details eigenvalue distributions and correlations for unitary, dissipative, and combined quantum dynamics.

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Area of Science:

  • Quantum Physics
  • Quantum Information Science
  • Statistical Mechanics

Background:

  • Open quantum systems are fundamental to understanding realistic quantum phenomena.
  • The Lindblad equation accurately models Markovian dynamics in these systems.
  • The Lindblad superoperator dictates the evolution of quantum states.

Purpose of the Study:

  • To investigate the spectral properties of the Lindblad superoperator.
  • To apply random-matrix theory to understand eigenvalue distributions and correlations.
  • To analyze these properties for different types of quantum dynamics.

Main Methods:

  • Application of random-matrix theory to the Lindblad superoperator.
  • Analysis of eigenvalue distributions.
  • Calculation of correlations between neighboring eigenvalues.

Main Results:

  • Spectral properties were elucidated using random-matrix theory.
  • Eigenvalue distributions were obtained for unitary dynamics, pure dissipation, and combined dynamics.
  • Correlations of neighboring eigenvalues were analyzed for these dynamics.

Conclusions:

  • Random-matrix theory provides insights into the spectral characteristics of quantum dynamics.
  • The study characterizes the behavior of open quantum systems under various dynamical regimes.
  • Findings contribute to the theoretical understanding of quantum information processing and quantum thermodynamics.