Quantum phase transitions in the quasi-periodic kicked rotor

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We present a microscopic theory of transport in quasi-periodically 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 Planck's constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we derive the microscopic theory of the ensuing localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a `super-metal'. Signatures of the corresponding metal/super-metal transition are discussed.