Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards

Details Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards

1999-06-10

arxiv.org/abs/chao-dyn/9906018v1

Nonlinear Sciences

Chaotic Dynamics

11 pages, 5 figures

Scientific paper

10.1103/PhysRevE.61.6434

An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling relations for the average complexity of symbolic trajectories are formally the same as those governing the semi-classical limit of quantum systems. Two cases-the circle, and the stadium-are examined in detail, and are presented as paradigms.

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