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      Partner orbits and action differences on compact factors of the hyperbolic plane. II: Higher-order encounters

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          Abstract

          Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. We specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. The companion paper [Huynh and Kunze, 2015] proved the existence of a unique periodic partner orbit for a given periodic orbit with a small-angle self-crossing in configuration space that is a 2-encounter and derived an estimate for the action difference of the orbit pair. In this paper, we provide an inductive argument to deal with higher-order encounters: we prove that a given periodic orbit including an \(L\)-parallel encounter has \((L-1)!-1\) partner orbits; we construct partner orbits and give estimates for the action differences between orbit pairs.

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          Author and article information

          Journal
          2015-01-18
          2016-02-21
          Article
          10.1016/j.physd.2015.10.001
          1501.04289
          057942e7-58a4-4cc2-b384-658585101666

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          37C27, 37D20, 37D40, 81Q50
          Physica D 314 (2016) 35-53
          final version Remark 3.3 was added
          math-ph math.MP

          Mathematical physics,Mathematical & Computational physics
          Mathematical physics, Mathematical & Computational physics

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