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In classical Drude theory the conductivity is determined by the mass of thepropagating particles and the mean free path between two scattering events. Fora quantum particle this simple picture of diffusive transport loses relevanceif strong correlations dominate the particle motion. We study a situation wherethe propagation of a fermionic particle is possible only through creation andannihilation of local bosonic excitations. This correlated quantum transportprocess is outside the Drude picture, since one cannot distinguish between freepropagation and intermittent scattering. The characterization of transport ispossible using the Drude weight obtained from the f-sum rule, although itsinterpretation in terms of free mass and mean free path breaks down. For thesituation studied we calculate the Green's function and Drude weight using aGreen's functions expansion technique, and discuss their physical meaning.

Analytical calculation of the Green's function and Drude weight for a correlated fermion-boson system