Julia set describes quantum tunnelling in the presence of chaos

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

Research output: Contribution to journalArticle

37 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
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number17
DOIs
Publication statusPublished - May 3 2002

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Julia set
Chaos theory
chaos
Chaos
dynamical systems
Complex Dynamical Systems
Standard Map
Dynamical systems
Transitivity
Trajectories
trajectories
Propagator
propagation
Trajectory
Path

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Julia set describes quantum tunnelling in the presence of chaos. / Shudo, A.; Ishii, Yutaka; Ikeda, K. S.

In: Journal of Physics A: Mathematical and General, Vol. 35, No. 17, 03.05.2002.

Research output: Contribution to journalArticle

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