Julia set describes quantum tunnelling in the presence of chaos

A. Shudo, Y. Ishii, K. S. Ikeda

    Research output: Contribution to journalArticlepeer-review

    43 Citations (Scopus)

    Abstract

    We find that characteristics of quantum tunnelling in the presence of chaos can be regarded as a manifestation of the Julia set of the complex dynamical system. Several numerical pieces of evidence for the standard map, together with a rigorous statement for the Hénon map, are presented, demonstrating that the complex classical paths which contribute to the semiclassical propagator are dense in the Julia set. Chaotic tunnelling can thus be characterized by the transitivity of the dynamics and high density of the trajectories on the Julia set.

    Original languageEnglish
    Pages (from-to)L225-L231
    JournalJournal of Physics A: Mathematical and General
    Volume35
    Issue number17
    DOIs
    Publication statusPublished - May 3 2002

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • General Physics and Astronomy

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