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 $w(t,L)$ has a scaling behavior $w(t,L)=L^{3/4}f(t/L^{9/4})$, with $f\left(u\right)$ constant for $u\gg 1$ and $f\left(u\right)\sim u^{1/3}$ for $u\ll 1$. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent $9/4$ is a new dynamical exponent for relaxation processes in driven diffusive systems.