4 research outputs found
Semiclassical Inequivalence of Polygonalized Billiards
Polygonalization of any smooth billiard boundary can be carried out in
several ways. We show here that the semiclassical description depends on the
polygonalization process and the results can be inequivalent. We also establish
that generalized tangent-polygons are closest to the corresponding smooth
billiard and for de Broglie wavelengths larger than the average length of the
edges, the two are semiclassically equivalent.Comment: revtex, 4 ps figure
Slow relaxation in weakly open vertex-splitting rational polygons
The problem of splitting effects by vertex angles is discussed for
nonintegrable rational polygonal billiards. A statistical analysis of the decay
dynamics in weakly open polygons is given through the orbit survival
probability. Two distinct channels for the late-time relaxation of type
1/t^delta are established. The primary channel, associated with the universal
relaxation of ''regular'' orbits, with delta = 1, is common for both the closed
and open, chaotic and nonchaotic billiards. The secondary relaxation channel,
with delta > 1, is originated from ''irregular'' orbits and is due to the
rationality of vertices.Comment: Key words: Dynamics of systems of particles, control of chaos,
channels of relaxation. 21 pages, 4 figure