Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems

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 $w(t,L)=L^{3\mathrm{/}4}f(t\mathrm{/}{L}^{9\mathrm{/}4})$, with $f(u)$ constant for $u\gg 1$ and $f(u)\sim u^{1\mathrm{/}3}$ for $u\ll 1$. 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.