Calculation of superdiffusion for the Chirikov-Taylor model.
It is widely known that the paradigmatic Chirikov-Taylor model presents enhanced diffusion for specific intervals of its stochasticity parameter due to islands of stability, which are elliptic orbits surrounding accelerator mode fixed points. In contrast with normal diffusion, its effect has never been analytically calculated. Here, we introduce a differential form for the Perron-Frobenius evolution operator in which normal diffusion and superdiffusion are treated separately through phases formed by angular wave numbers. The superdiffusion coefficient is then calculated analytically resulting in a Schloemilch series with an exponent beta=3/2 for the divergences. Numerical simulations support our results.
Venegeroles
Roberto
R
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, SP, Brazil. roberto.venegeroles@ufabc.edu.br