Exact Solution of the Macroscopic Fluctuation Theory for the Symmetric Exclusion Process

We present the first exact solution for the time-dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the inverse scattering method. For the step initial condition with two densities, we obtain exact and compact formulas for the optimal density profile and the response field that produce a required fluctuation, both at initial and final times. The large deviation function of the current is derived and coincides with the formula obtained previously by microscopic calculations. This provides the first analytic confirmation of the validity of the MFT for an interacting model in the time-dependent regime.