Onset of diffusion in the kicked Harper model

Fabio Tal

Abstract:

We study a standard two-parameter family of area-preserving torus diffeomorphisms, known as the kicked Harper model in theoretical physics, by a combination of topological arguments and KAM-theory. We concentrate on the structure of the parameter sets where the rotation set has empty and non-empty interior, respectively, and describe their qualitative properties and scaling behaviour both for small and large parameters. This confirms numerical observations about the onset of diffusion in the physics literature. As a byproduct, we obtain the continuity of the rotation set within the class of Hamiltonian torus homeomorphisms.
This is Joint work w. T. Jäger and A. Koropecki