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Related Experiment Videos

Resonance-assisted tunneling in near-integrable systems.

O Brodier1, P Schlagheck, D Ullmo

  • 1Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), 91405 Orsay Cedex, France.

Physical Review Letters
|August 11, 2001
PubMed
Summary

Dynamical tunneling in near-integrable systems is altered by classical resonances, deviating from purely exponential decay. This study quantifies these deviations using a semiclassical model for eigenvalue splitting.

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Mathematical physics

Background:

  • Dynamical tunneling describes quantum transitions between classically isolated regions.
  • Near-integrable systems exhibit complex behavior influenced by both regular and chaotic dynamics.
  • The kicked Harper model is a standard testbed for studying quantum dynamics in periodically driven systems.

Purpose of the Study:

  • To investigate dynamical tunneling in near-integrable regimes.
  • To analyze the influence of classical resonances on wave function decay.
  • To develop a semiclassical framework for predicting eigenvalue splitting.

Main Methods:

  • Studying the kicked Harper model.
  • Analyzing wave function decay in classically forbidden regions.

Related Experiment Videos

  • Developing a semiclassical model incorporating resonance substructure.

    • Main Results:

    • Classical resonances modify exponential wave function decay.
    • Eigenvalue splitting deviates significantly from integrable predictions.
    • The semiclassical framework accurately reproduces observed eigenvalue splitting behavior.

    Conclusions:

    • Classical resonances play a crucial role in dynamical tunneling.
    • The developed semiclassical model provides quantitative predictions for eigenvalue splitting.
    • Understanding these mechanisms is key for quantum chaos studies.