Irregular Scattering of Particles Confined to Ring-Bounded Cavities
نویسنده
چکیده
The classical motion of a Ii"ee particle that scatters elastically from ring-bounded cavities is analyzed nunaerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed of N scatrefers the Ilow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically with N, which is consistent with the theoretical derivation of Chernov for polygon-shaped billiard systems. The escape time from cavities bounded by a ring of N separated scatterers is demonstrated to follow a geometric distribution as a function of the aperture size. An empirical scaling is proposed between the Lyapunov exponent, the escape time, and N.
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