Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system

Anupam Kundu

Published 2022-09-16Version 1

We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium that is slightly deviated from an underlying global equilibrium, we estimate the correction to the local equilibrium distribution. This correction arises mainly through the space-time correlations of the local currents. In the continuum limit, we show that the local equilibrium distribution along with the correction yields drift-diffusion equation for the `volume' and super-diffusion equation for the energy in the linear response regime as macroscopic hydrodynamics. We find explicit expression of the super-diffusion equation. Further, we find diffusive correction to the super-diffusive evolution. Such a correction allows us to study a crossover from diffusive to anomalous transport. We demonstrate this crossover numerically through the system size scaling of the stationary current in non-equilibrium steady state prepared by two reservoirs of different temperatures.