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The model, which we call a random billiard, is an example of a random dynamical system based on the idea of a billiard system with geometric microstructure.
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Even though the energy level statistics for quantum billiards in the semi-classical counterparts to classical billiard systems share universal properties, the actual behavior of the trajectories in the two systems is substantially different (under Schrödinger evolution Hilbert space vectors never diverge from one another).
Billiard systems are used in statistical physics as models of particle motion.
This work is connected to more-recent work by Avila and Vincent Delecroix, which investigates mixing in regular polygonal billiard systems.
The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum chaos research.
Whereas mechanistic materialism views nature as an organized system of billiard balls, Mach's evolutionary perspective viewed nature as a dynamic process.
Standard examples of analogical models include the hydraulic model of an economic system, the billiard ball model of a gas, the computer model of the mind or the liquid drop model of the nucleus.
Mr. Hunt has developed other high-class establishments, including Amsterdam Billiards, a billiard parlor.
The cat map, for instance, is a C-system that is also a K-system (Lichtenberg & Liebermann, 1992, p. 307); but there are K-systems such as the so-called stadium billiard which are not C-systems (Ott, 1993, p. 262).
We describe the elements to construct an interactive computer system which helps train billiard players in enhancing their skills.
A low cost training system is proposed for regular billiard game tutoring.
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