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Julia set describes quantum tunnelling in the presence of chaos

2002/04/19 by Akira Shudo, A. Shudo, Yutaka Ishii +3
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaos-based Image/Signal Encryption #Quantum chaos and dynamical systems #nlin.CD

paper · pdf · doi:10.1088/0305-4470/35/17/101

published as J. Phys. A vol. 35 (2002) L31-L43

openalex publication_date 2002/04/19 · arxiv created 2002/05/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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.

Citations