Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1995-02-03
Nonlinear Sciences
Chaotic Dynamics
32 pages, compressed with gzip / uuencode
Scientific paper
This paper is devoted to the quantum chaology of three-dimensional systems. A trace formula is derived for compact polyhedral billiards which tessellate the three-dimensional hyperbolic space of constant negative curvature. The exact trace formula is compared with Gutzwiller's semiclassical periodic-orbit theory in three dimensions, and applied to a tetrahedral billiard being strongly chaotic. Geometric properties as well as the conjugacy classes of the defining group are discussed. The length spectrum and the quantal level spectrum are numerically computed allowing the evaluation of the trace formula as is demonstrated in the case of the spectral staircase N(E), which in turn is successfully applied in a quantization condition.
Aurich Ralf
Marklof Jens
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