Activity driven transport in harmonic chains

How the transport properties of an extended system is affected by coupling to active reservoirs is a significant, yet virtually unexplored question. Here we address this issue in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators. The couplings to the reservoirs, which exert correlated stochastic forces on the boundary oscillators, lead to fascinating behavior of the energy current and kinetic temperature profile, which we compute exactly in the thermodynamic limit. We show that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. For the example of a dichotomous active force, we find the physical origin of the NDC using nonequilibrium response formalism. It turns out that the kinetic temperature profile remains uniform at the bulk, and can be expressed in a form similar to the thermally driven case. We show that despite this apparent similarity, no effective thermal picture can be consistently built in general. However, such a picture emerges in the small activity limit, where many of the well-known results are recovered.