Abstract
We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant, . We show here that for rational values of , it bears a similarity to a disordered metallic ring of circumference q and threaded by an Aharonov–Bohm flux. Building on this correspondence, we obtain quantitative results for the time-dependent behavior of the QKR kinetic energy, (this is an observable that sensitively probes the system's localization properties). For values of q smaller than the localization length ξ, we obtain scaling , where Δ=2π/q is the quasi-energy level spacing on the ring. This scaling is indicative of a long time dynamics that is neither localized nor diffusive. For larger values q≫ξ, the functions saturate (up to exponentially small corrections ∼exp(−q/ξ)), thus reflecting essentially localized behavior.
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