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

R. Aurich·T. Hesse·F. Steiner
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Abstract

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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R. Aurich, T. Hesse, F. Steiner. 1994-11-29. On the Role of Non-Periodic Orbits in The Semiclassical Quantization of the Truncated Hyperbola Billiard. https://doi.org/10.1103/physrevlett.74.4408

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