Phase transition in equilibrium fluctuations of symmetric slowed exclusion

We analyze the equilibrium fluctuations of density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is α n − β , with α > 0 , β ∈ [ 0 , + ∞ ] and n is the scaling parameter. Depending on the regime of β , we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value β = 1 , starting a tagged particle near the slow bond, we obtain a family of Gaussian processes indexed in α , interpolating a fractional Brownian motion of Hurst exponent 1 / 4 and the degenerate process equal to zero.