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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Quantum chaos

Background:

  • The out-of-time-order correlator (OTOC) measures information scrambling in quantum systems.
  • In one-body systems, OTOC relaxation relates to Ruelle-Pollicott resonances.
  • For many-body systems, the Liouvillian spectrum of open extensions governs OTOC relaxation.

Purpose of the Study:

  • To investigate the relationship between OTOC decay and the Liouvillian spectrum in a closed many-body system.
  • To determine if the Liouvillian gap predicts OTOC relaxation rates in the kicked Ising spin chain.

Main Methods:

  • Studied the kicked Ising spin chain, a paradigmatic many-body quantum system.
  • Analyzed the Liouvillian spectrum of weakly open extensions of the system's dynamics.
  • Calculated the OTOC decay rates in the isolated (closed) system.

Main Results:

  • The long-time exponential decay rate of the OTOC in the closed system equals twice the intrinsic Liouvillian gap.
  • This correspondence holds across different parameter regimes with varying level spacing statistics.
  • Demonstrated a robust connection between the Liouvillian spectrum and OTOC dynamics.

Conclusions:

  • The Liouvillian spectrum provides a universal framework for understanding relaxation and irreversibility in closed many-body quantum systems.
  • The Liouvillian gap is a key predictor of quantum information scrambling rates, as quantified by OTOC decay.