SUBDIFFUSIVE AND SUPERDIFFUSIVE QUANTUM TRANSPORT AND GENERALIZED DUALITY

As a generic model for transport of interacting fermions through a bar rier or interstitials in a lattice, quantum Brownian motion in a perio dic potential is studied. There is a duality transformation between th e continuous coordinate or phase representation and the discrete momen tum or charge representation for general frequency-dependent damping. Sub-Ohmic friction is mapped on super-Ohmic friction, and vice versa. The mapping is exact for arbitrary barrier height and valid at any tem perature. Thus all features of the continuous model can be investigate d from analytical or numerical analysis of the discrete model. Nonpert urbative results for the frequency-dependent linear mobility including subdiffusive and superdiffusive behaviors are reported.