Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards
chao-dyn
2009-10-31 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9906018,
title = {Quantum Algorithmic Integrability: The Metaphor of Polygonal Billiards},
author = {Giorgio Mantica},
journal= {arXiv preprint arXiv:chao-dyn/9906018},
year = {2009}
}
Comments
11 pages, 5 figures