We show that domain walls separating coexisting extremal current phases in
driven diffusive systems exhibit complex stochastic dynamics, with a
subdiffusive temporal growth of position fluctuations due to long-range
anticorrelated current fluctuations and a weak pinning at long times. This weak
pinning manifests itself in a saturated width of the domain wall position
fluctuations that increases sublinearly with the system size. As a function of
time t and system size L, the width w(t,L) exhibits a scaling behavior
w(t,L)=L3/4f(t/L9/4), with f(u) constant for u≫1 and f(u)∼u1/3 for u≪1. An Orstein-Uhlenbeck process with long-range
anticorrelated noise is shown to capture this scaling behavior. Results for the
drift coefficient of the domain wall motion point to memory effects in its
dynamics.Comment: 6 pages, 4 figures plus 6 pages supplemental material with 3 figure