Quantum algorithmic integrability: the metaphor of classical polygonal billiards
We study the algorithmic complexity of motions in classical polygonal billiards, which, as the number of sides increases, tend to curved billiards, both regular and chaotic. This study unveils the equivalence of this problem to the procedure of quantization: the average complexity of symbolic trajectories in polygonal billiards features the same scaling relations (with respect to the number of sides) that govern quantum systems when a semiclassical parameter is varied. Two cases, the polygonal approximations of the circle and of the stadium, are examined in detail and are presented as paradigms of quantization of integrable and chaotic systems.
Mantica
G
International Center for the Study of Dynamical Systems, Universita della Insubria, via Lucini 3, 22100 Como, Italy; and Istituto Nazionale di Fisica della Materia, Unita di Milano; and Istituto Nazionale di Fisica Nucleare, sezione di Milan.