Corrections to quasilinear diffusion in area-preserving maps

Publisher Website
Google Scholar
Abstract
Higher-order corrections to the quasilinear diffusion coefficient are obtained for Hamiltonian maps which are locally approximated by the standard map. Using the Fermi map [E. Fermi, Phys. Rev. 75, 1169 (1949); M. A. Lieberman and A. J. Lichtenberg, Phys. Rev. A 5, 1852 (1972)] as an example, we numerically integrate the Fokker-Planck equation for the action and compare the resulting distribution function with direct solutions of the mapping equations. The second moment of the distribution is compared with the diffusion measured in the numerical experiments. Both show oscillations (as a function of the initial velocity) similar to those found in the standard map. In addition, we numerically find the invariant distribution in the Fermi map. We observe dips in the distribution of actions. We calculate the size of islands surrounding stable fixed points and show that the dips correspond to these islands. Thus chaotic orbits uniformly fill the phase space available to them.