Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards
arXiv:chao-dyn/9906018 · doi:10.1103/PhysRevE.61.6434
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.
11 pages, 5 figures