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Structure of resonance eigenfunctions for chaotic systems with partial escape.

Konstantin Clauß1, Eduardo G Altmann2, Arnd Bäcker1,3

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Summary

This study introduces classical measures to understand chaotic quantum systems with partial escape. These measures accurately describe quantum eigenfunctions, bridging classical and quantum dynamics.

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Area of Science:

  • Quantum mechanics
  • Dynamical systems theory
  • Statistical physics

Background:

  • Physical systems often exhibit partial escape or absorption, defying purely closed or open models.
  • Understanding resonance eigenfunctions in chaotic quantum systems with partial escape is crucial.

Purpose of the Study:

  • Introduce novel classical measures for chaotic quantum systems with partial escape.
  • Explain key properties of resonance eigenfunctions using these classical measures.
  • Investigate the relationship between classical and quantum dynamics in systems with partial decay.

Main Methods:

  • Construct a family of conditionally invariant measures by interpolating forward and backward dynamics.
  • Utilize varying decay rates to parameterize the measures.
  • Perform numerical simulations on a representative chaotic quantum system.

Main Results:

  • Classical measures accurately capture multifractal phase-space distributions of quantum eigenfunctions.
  • The product structure of eigenfunctions along stable and unstable directions is explained.
  • The dependence of eigenfunctions on the decay rate is correctly described.
  • The Jensen-Shannon distance between classical and quantum measures approaches zero for long- and short-lived eigenfunctions in the semiclassical limit.

Conclusions:

  • The developed classical measures provide a robust framework for analyzing chaotic quantum systems with partial escape.
  • These measures offer insights into the semiclassical behavior of quantum eigenfunctions.
  • The study highlights the power of classical dynamics in describing quantum phenomena in systems with dissipation.