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Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential

Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan
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Condens. Matter 2020, 5(1), 1; https://doi.org/10.3390/condmat5010001
Received: 15 December 2019 / Revised: 24 December 2019 / Accepted: 27 December 2019 / Published: 30 December 2019
(This article belongs to the Special Issue Many Body Quantum Chaos)
We show that a two-dimensional area-preserving map with Lorentzian potential is a topological horseshoe and uniformly hyperbolic in a certain parameter region. In particular, we closely examine the so-called sector condition, which is known to be a sufficient condition leading to the uniformly hyperbolicity of the system. The map will be suitable for testing the fractal Weyl law as it is ideally chaotic yet free from any discontinuities which necessarily invokes a serious effect in quantum mechanics such as diffraction or nonclassical effects. In addition, the map satisfies a reasonable physical boundary condition at infinity, thus it can be a good model describing the ionization process of atoms and molecules. View Full-Text
Keywords: periodically kicked system; Lorentzian potential; topological horseshoe; uniformly hyperbolicity; sector condition; fractal Weyl law periodically kicked system; Lorentzian potential; topological horseshoe; uniformly hyperbolicity; sector condition; fractal Weyl law
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Yoshino, H.; Kogawa, R.; Shudo, A. Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential. Condens. Matter 2020, 5, 1.

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