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Out-of-time-order correlators (OTOCs) in open quantum systems with discrete energy levels saturate to a constant value. This contrasts with quantum-chaotic systems, offering insights into quantum dynamics and decoherence.

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Area of Science:

  • Quantum Mechanics
  • Statistical Physics
  • Condensed Matter Physics

Background:

  • Out-of-time-order correlators (OTOCs) are sensitive probes of quantum chaos and scrambling.
  • Open quantum systems describe realistic physical scenarios where systems interact with their environment.
  • Disordered interacting media present complex quantum dynamics relevant to condensed matter phenomena.

Purpose of the Study:

  • To investigate the behavior of OTOCs in quantum systems coupled to a dissipative environment.
  • To contrast the dynamics of OTOCs in discrete-level systems with those in quantum-chaotic systems.
  • To analyze the influence of dephasing and inelastic transitions on OTOC decay times.

Main Methods:

  • Theoretical analysis of OTOCs for a quantum system weakly coupled to a dissipative environment.
  • Focusing on systems with discrete energy levels, particularly two-level systems.
  • Microscopic calculation of decay times and saturation constants for OTOCs.

Main Results:

  • OTOCs in discrete-level systems saturate to a constant value at long times, unlike the exponential growth in quantum-chaotic systems.
  • Decay times of OTOCs are determined by inelastic transitions and pure dephasing processes.
  • For classical environments, OTOC evolution maps to the density matrix evolution of two coupled systems.

Conclusions:

  • Dissipative environments lead to saturation of OTOCs in discrete-level systems, indicating a suppression of chaos.
  • The distinct time scales associated with different decay mechanisms provide a way to probe system-environment interactions.
  • The study offers a model for understanding quantum dynamics in realistic, open systems.