PERIODIC-ORBITS IN QUANTUM STANDARD MAPS

The importance of periodic orbits, both elliptic and hyperbolic, in analyzing driven quantum systems is now well established. We present a detailed analysis of the quantum mechanics in the vicinity of these orbits for both a piecewise-linear and the original standard maps. We begin by constructing effective Hamiltonian operators valid locally near nondegenerate periodic orbits. Our general formula allows for the calculation of the quasienergy spectrum near elliptic orbits as well as of the strength of scarring on hyperbolic orbits. Preliminary results on the dependence of this measure of scarring on the instability of the classical orbit and on h are also presented.