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Localization in chaotic systems with a single-channel opening.

Domenico Lippolis1,2, Jung-Wan Ryu2,3, Sang Wook Kim4

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Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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We found that introducing a single channel opening into quantum chaotic systems causes wave function localization. This deviation from random matrix theory predictions is observed even in the semiclassical limit.

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Area of Science:

  • Quantum chaos
  • Statistical mechanics
  • Wave phenomena

Background:

  • Random matrix theory (RMT) accurately describes complex quantum systems.
  • Understanding wave function behavior in open quantum systems is crucial.
  • Previous studies have not fully explored localization effects in open quantum maps.

Purpose of the Study:

  • To investigate wave function localization in a quantum chaotic system with a single-channel opening.
  • To analyze deviations from RMT predictions in the presence of an open channel.
  • To explore the relationship between wave function properties and decay rates.

Main Methods:

  • Introduction of a single-channel opening into a random Hamiltonian and a quantized chaotic map.
  • Analysis of wave function statistics and localization phenomena.
  • Derivation and testing of a linear relation between wave function intensities and decay rates.
  • Comparison with predictions from random matrix theory and the Breit-Wigner law.

Main Results:

  • Observed localization on the opening, deviating from RMT predictions even in the semiclassical limit.
  • Identified fast-decaying states localized on the opening and long-lived states suppressed at the opening.
  • Established a linear relation between wave function intensities and decay rates for long-lived states, analogous to the Breit-Wigner law.
  • Found similar behavior in the classical propagator's eigenfunctions only in the weak-coupling regime.

Conclusions:

  • A single-channel opening induces significant deviations in wave function statistics within quantum chaotic systems.
  • The system exhibits distinct behaviors for fast-decaying and long-lived states, with implications for resonance phenomena.
  • The derived linear relation offers a new perspective on wave function decay in open quantum systems.