Fractal analysis of chaotic classical scattering in a cut-circle billiard with two openings

Ree, Suhan; Reichl, L. E.

doi:10.1103/physreve.65.055205

Cited by 16 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Leakage reveals the foliations inside the closed system (Aguirre and Sanjuán, 2003;Aguirre et al, 2009;Sanjuán et al, 2003;Schneider et al, 2002) that lead, e.g., to fractal exit boundaries (Bleher et al, 1988;Portela et al, 2007;Ree and Reichl, 2002).…”

Section: Applicationsmentioning

confidence: 99%

Leaking chaotic systems

2013

View full text Add to dashboard Cite

There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. A unified treatment of leaking systems is provided and applications to different physical problems, in both the classical and quantum pictures, are reviewed. The treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption and/or transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima çon family of billiards illustrate the main text. Regarding billiard dynamics, it is emphasized that a correct discrete-time representation can be given only in terms of the so-called true-time maps, while traditional Poincaré maps lead to erroneous results. Perron-Frobenius-type operators are generalized so that they describe true-time maps with partial leaks

show abstract

Section: Applicationsmentioning

confidence: 99%

Leaking chaotic systems

2013

View full text Add to dashboard Cite

show abstract

“…To investigate the chaotic escape quantitatively within the framework of the box-counting method [34] for the ionization of Rydberg atoms in external fields, the fractal dimension of the self-similarity structure that reflects the chaotic properties is defined as…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Fractal dynamics in the ionization of helium Rydberg atoms

Zhang

et al. 2016

Chinese Phys. B

View full text Add to dashboard Cite

We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory. By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization, we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons, and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy. We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons. Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field, and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms. It is shown that, besides the electric and magnetic fields, core scattering is a primary factor in the fractal dynamics.

show abstract

“…We take the black areas as a subset nested in (0𝜋/2). [11] We set 𝑎 3 = 0.5 to observe the similarity of the singular point. Because just watching similarity, we suppose the number of collisions of the singular point is 1 and the number of collisions of the nonsingular point is 0.…”

Section: 𝐸𝑗+1−𝐸𝑗 𝐷mentioning

confidence: 99%

Fractal Analysis of Transport Properties in a Sinai Billiard

Jiang

Zhang

Bian

et al. 2011

Chinese Phys. Lett.

View full text Add to dashboard Cite

Research contacting chaos with fractals is carried out. First, we employ the theoretical quarter Sinai billiard model to study its chaos by using the stationary expansion method. When the billiard is chaotic, the singular point shows self-similarity. We further utilize the method of simplified box counting to calculate the fractal dimension. The result evidently proves the self-similarity of the singular point before escaping from a potential well.

show abstract

Fractal analysis of chaotic classical scattering in a cut-circle billiard with two openings

Cited by 16 publications

References 17 publications

Leaking chaotic systems

Leaking chaotic systems

Fractal dynamics in the ionization of helium Rydberg atoms

Fractal Analysis of Transport Properties in a Sinai Billiard

Contact Info

Product

Resources

About