Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential
| Autor: | Ryota Kogawa, Hajime Yoshino, Akira Shudo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Diffraction
media_common.quotation_subject uniformly hyperbolicity Chaotic Classification of discontinuities 01 natural sciences 010305 fluids & plasmas Fractal lorentzian potential 0103 physical sciences Boundary value problem 010306 general physics media_common Physics Scattering Mathematical analysis Condensed Matter Physics Infinity sector condition lcsh:QC1-999 Electronic Optical and Magnetic Materials periodically kicked system Weyl law fractal weyl law topological horseshoe lcsh:Physics |
| Zdroj: | Condensed Matter, Vol 5, Iss 1, p 1 (2019) Condensed Matter Volume 5 Issue 1 |
| ISSN: | 2410-3896 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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