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Chaos and dynamical complexity in the quantum to classical transition.

Bibek Pokharel1, Moses Z R Misplon1, Walter Lynn1

  • 1Department of Physics and Astronomy, Carleton College, Northfield, Minnesota, 55057, USA.

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|February 3, 2018
PubMed
Summary

We investigated quantum system complexity and Lyapunov exponents (λ) in driven double-well oscillators. Quantum systems can exhibit greater chaos than their classical counterparts, even in experimentally accessible regimes.

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Area of Science:

  • Quantum mechanics
  • Quantum chaos
  • Nonlinear dynamics

Background:

  • Open quantum systems exhibit complex dynamics influenced by environmental coupling.
  • Lyapunov exponents (λ) quantify the sensitivity to initial conditions, a hallmark of chaos.

Purpose of the Study:

  • To investigate the relationship between environmental coupling (Γ) and effective Planck's constant (β²) on dynamical complexity and Lyapunov exponents (λ) in an open quantum driven double-well oscillator.
  • To explore quantum chaos in systems where the classical limit is regular.

Main Methods:

  • Analysis of the largest Lyapunov exponents (λ) and dynamical complexity.
  • Mapping the dependence on coupling to the environment (Γ) and effective Planck's constant (β²).

Main Results:

  • Lyapunov exponents (λ) generally increase with effective Hilbert space size (decreasing β).
  • Quantum systems can display greater chaos (λ) than their classical counterparts, even when the classical system is regular.
  • Discovered quantum chaotic attractors with no classical analogues.

Conclusions:

  • The correspondence limit can be challenging for classically chaotic systems, contrary to standard assumptions.
  • Quantum chaos phenomena are observable in experimentally accessible regimes.