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On complex dynamics in a Suris's integrable map
Version 1
: Received: 29 March 2024 / Approved: 29 March 2024 / Online: 1 April 2024 (10:14:39 CEST)
A peer-reviewed article of this Preprint also exists.
Hanada, Y.; Shudo, A. Quantum Tunneling and Complex Dynamics in the Suris’s Integrable Map. Entropy 2024, 26, 414. Hanada, Y.; Shudo, A. Quantum Tunneling and Complex Dynamics in the Suris’s Integrable Map. Entropy 2024, 26, 414.
Abstract
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map and the associated Hamiltonian system is qualitatively the same, with only a slight difference in magnitude. However, the tunneling tails of the wave functions, obtained by superposing the eigenfunctions that form the doublet, exhibit significant difference. To explore the origin of the difference, we observe the classical dynamics in the complex plane and find that the existence of branch points appearing in the potential function of the integrable map could play the role for yielding non-trivial behavior in the tunneling tail. The result highlights the subtlety of quantum tunneling, which cannot be captured in nature only by the dynamics in the real plane.
Keywords
dynamical tunneling; integrable map; complex classical dynamics
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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