Stadium Billiards with Energy-Dependent Mixed Boundary Conditions | Zendy

Naotaka Yoshinaga | Zendy; Kiyoshige Matsumura | Zendy; Mitsuyoshi Tomiya | Zendy

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Stadium Billiards with Energy-Dependent Mixed Boundary Conditions

Author(s) -

Naotaka Yoshinaga,

Kiyoshige Matsumura,

Mitsuyoshi Tomiya

Publication year - 1997

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.98.869

Subject(s) - dynamical billiards , semiclassical physics , physics , boundary (topology) , stadium , boundary value problem , spectrum (functional analysis) , classical mechanics , parametric statistics , quantum , energy spectrum , mathematical analysis , quantum mechanics , geometry , mathematics , statistics

A semiclassical theory is developed for billiards with energy-dependent mixed boundary conditions. Explicit expressions are derived for the smooth and oscillatory parts of the level density. The parametric dependence of the spectrum on the boundary conditions provides us a very useful tool in analyzing the classical and quantum correspondence in billiard systems. This is illustrated in the numerical analysis of the spectrum of the stadium billiard that has mixed boundary conditions on the circular parts.

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