Subdiffusive and superdiffusive quantum transport and generalized duality

TL;DR

This paper investigates quantum transport of interacting fermions in a lattice, revealing a duality transformation between different representations that maps sub-Ohmic to super-Ohmic friction, enabling analysis of complex diffusive behaviors.

Contribution

It introduces an exact duality transformation between continuous and discrete models for quantum Brownian motion, allowing analysis of subdiffusive and superdiffusive transport.

Findings

Exact duality maps sub-Ohmic to super-Ohmic friction.

New nonperturbative results for frequency-dependent mobility.

Analysis of subdiffusive and superdiffusive behaviors.

Abstract

As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or phase representation and the discrete momentum 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 temperature. Thus all features of the continuous model can be investigated from analytical or numerical analysis of the discrete model. New nonperturbative results for the frequency-dependent linear mobility including subdiffusive and superdiffusive behaviors are reported.