TUNNELING AND THE BAND-STRUCTURE OF CHAOTIC SYSTEMS

We compute the dispersion laws of chaotic periodic systems using the s emiclassical periodic orbit theory to approximate the trace of the pow ers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate cond uction processes through tunneling mechanisms. The results obtained, i llustrated with the kicked-Harper model, are in excellent agreement wi th numerical simulations, even in the extreme quantum regime.