On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

Details On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard

1994-11-29

arxiv.org/abs/chao-dyn/9411023v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, uu-encoded ps-file

Scientific paper

10.1103/PhysRevLett.74.4408

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, non-periodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.

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