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 αn−βαn−β, with α>0α>0, β∈[0,+∞]β∈[0,+∞] and nn is the scaling parameter. Depending on the regime of ββ, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value β=1β=1, starting a tagged particle near the slow bond, we obtain a family of Gaussian processes indexed in αα, interpolating a fractional Brownian motion of Hurst exponent 1/41/4 and the degenerate process equal to zero.