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Area of Science:

  • Quantum Chaos
  • Open Quantum Systems
  • Random Matrix Theory

Background:

  • Understanding the dynamics of chaotic quantum systems interacting with noisy environments is crucial.
  • Previous studies have explored spectral properties but often without a focus on asymptotic decay rates in the thermodynamic limit.

Purpose of the Study:

  • To investigate the decay rates of chaotic quantum systems coupled to noise.
  • To analyze the spectral properties of the Liouvillian superoperator under various random-matrix ensembles.
  • To identify the emergence and nature of spectral gaps and midgap states.

Main Methods:

  • Modeling the Hamiltonian and system-noise coupling using random N×N Hermitian matrices.
  • Studying the spectral properties of the Liouvillian superoperator.
  • Analyzing various random-matrix ensembles and their thermodynamic limits (N→∞).

Main Results:

  • The asymptotic decay rate remains non-zero in the thermodynamic limit, indicating a gapped spectrum.
  • For finite N, the probability of a small spectral gap vanishes exponentially with system size N.
  • A sharp transition occurs with increasing dissipation strength, leading to isolated midgap states.

Conclusions:

  • Chaotic quantum systems coupled to noise maintain a non-zero decay rate, ensuring stability.
  • The existence of midgap states beyond a critical dissipation strength has implications for quantum information processing.
  • These findings are relevant for both theoretical understanding and experimental realization in quantum systems.