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.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jun;61(6 Pt A):6434-43. doi: 10.1103/physreve.61.6434.
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.
我们研究经典多边形台球运动的算法复杂性，随着边数增加，其趋向于规则和混沌的曲线台球。这项研究揭示了该问题与量子化过程的等价性：当一个半经典参数变化时，多边形台球中符号轨迹的平均复杂性呈现出与量子系统相同的标度关系（相对于边数）。详细研究了圆和体育场的多边形近似这两种情况，并将其作为可积和混沌系统量子化的范例呈现出来。
