Theory of the Anderson Transition in the Quasiperiodic Kicked Rotor

Abstract

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.