Current fluctuations in the weakly asymmetric exclusion process with open boundaries.

The additivity principle allows a calculation of current fluctuations and associated density profiles in large diffusive systems. We apply this principle to the weakly asymmetric exclusion process (WASEP). We also calculate the cumulant generating function of the current and the density profiles associated with rare currents in finite systems using a numerical approach based on the density matrix renormalization group. Comparison of the two approaches allows us to verify the validity of the additivity principle and to get insight into the finite size scaling theory for current fluctuations in the WASEP. No evidence for a dynamical phase transition is found.