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Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards

Giorgio Mantica
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Abstract

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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BibTeXRIS

Giorgio Mantica. 1999-06-10. Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards. https://doi.org/10.1103/physreve.61.6434

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