Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-06-14
Eur. Phys. J. B 30, 189 (2002)
Nonlinear Sciences
Chaotic Dynamics
25 pages, 18 figures
Scientific paper
10.1140/epjb/e2002-00374-7
Employing symbolic dynamics for geodesic motion on the tesselated pseudosphere, the so-called Hadamard-Gutzwiller model, we construct extremely long periodic orbits without compromising accuracy. We establish criteria for such long orbits to behave ergodically and to yield reliable statistics for self-crossings and avoided crossings. Self-encounters of periodic orbits are reflected in certain patterns within symbol sequences, and these allow for analytic treatment of the crossing statistics. In particular, the distributions of crossing angles and avoided-crossing widths thus come out as related by analytic continuation. Moreover, the action difference for Sieber-Richter pairs of orbits (one orbit has a self-crossing which the other narrowly avoids and otherwise the orbits look very nearly the same) results to all orders in the crossing angle. These findings may be helpful for extending the work of Sieber and Richter towards a fuller understanding of the classical basis of quantum spectral fluctuations.
Braun Peter A.
Haake Fritz
Heusler Stefan
Müller Sebastian
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