  We study a standard two-parameter family of area-preserving torus
diffeomorphisms, known in theoretical physics as the kicked Harper model, 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.
