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The maximum entropy principle is challenged by aperiodic drives. This study proves quantum systems driven by Thue-Morse sequences achieve strong quantum ergodicity, revealing critically slow dynamics in complex quantum systems.

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Area of Science:

  • Quantum Dynamics
  • Statistical Physics
  • Complex Systems

Background:

  • The maximum entropy principle is fundamental for analyzing complex dynamics.
  • Previous work suggested aperiodic drives, like the Thue-Morse drive, lead to nonergodic states, challenging this principle.
  • This tension arises from the apparent conflict between ergodicity and emergent nonergodic behaviors.

Purpose of the Study:

  • To resolve the apparent tension between the maximum entropy principle and findings on aperiodic drives.
  • To rigorously investigate the long-time behavior of quantum systems under the Thue-Morse drive.
  • To characterize the nature of emergent steady states and conserved quantities in driven quantum systems.

Main Methods:

  • Rigorous mathematical proof to demonstrate quantum ergodicity.
  • Analysis of time evolution of quantum states in the Hilbert space.
  • Numerical simulations to explore dynamics under various aperiodic drives.

Main Results:

  • The Thue-Morse drive leads to a strong form of quantum ergodicity in the long-time limit.
  • Quantum systems exhibit critically slow complete Hilbert-space ergodicity, approximating Floquet drives for extended periods.
  • This scale-free ergodic dynamics is not unique to the Thue-Morse drive but is observed with other morphic sequences.

Conclusions:

  • The study resolves the tension by proving eventual strong quantum ergodicity under aperiodic drives.
  • A new class of dynamics, critically slow complete Hilbert-space ergodicity, is identified in time-dependent quantum systems.
  • Full ergodicity is attained only after extremely long timescales, offering new insights into complex quantum dynamics.