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Quantum mechanics can create exponential instabilities in nonchaotic systems, challenging classical chaos predictions. This early-time quantum effect, measured by the out-of-time-ordered correlator (OTOC), appears even before quantum interference washes out classical chaos.

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Area of Science:

  • Quantum mechanics
  • Classical dynamics
  • Quantum chaos

Background:

  • Classical chaotic systems exhibit the butterfly effect, where small changes in initial conditions lead to large, exponential divergence.
  • Reconciling classical chaos with quantum mechanics is a central challenge in quantum chaos research.
  • Quantum-classical correspondence in dynamics typically breaks down quickly due to quantum interference.

Purpose of the Study:

  • To investigate if quantum mechanics can induce exponential instabilities in classically nonchaotic systems.
  • To explore the early-time dynamics of quantum systems using the out-of-time-ordered correlator (OTOC).
  • To compare quantum dynamics with classical dynamics in nonchaotic systems.

Main Methods:

  • Utilized the out-of-time-ordered correlator (OTOC) as a diagnostic tool.
  • Analyzed classically nonchaotic models, specifically polygonal billiards.
  • Calculated OTOC behavior at early times, considering Planck's constant dependence.

Main Results:

  • Demonstrated Lyapunov-like exponential growth of the OTOC in classically nonchaotic systems.
  • Observed Planck's-constant-dependent rates for this exponential growth.
  • Showcased a stark contrast between the rapid early-time OTOC growth in quantum systems and the slow growth in their classical counterparts.

Conclusions:

  • Quantum mechanics can generate exponential instabilities in classically nonchaotic systems within an early-time window.
  • The OTOC reveals violations of classical-to-quantum dynamical correspondence even before quantum interference effects become dominant.
  • This suggests a more complex relationship between classical chaos and quantum dynamics than previously understood.