Profile-driven interfaces in 1+1 dimensions: periodic steady states, dynamical melting and detachment

Abstract

We study the steady-state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity v_e. In the strong coupling limit, the problem maps onto an asymmetric exclusion process involving motion of particles in 1-d with position-dependent right and left jump probabilities. For small v_e, the interface is stuck to the field profile. As v_e increases the profile detaches from the interface. At the transition point (and beyond), the interfacial structure and dynamics are characterized by the KPZ exponents. For small v_e, on the other hand, the interface is macroscopically smooth with a vanishing roughness exponent α. The interfacial structure is periodic with a periodicity which depends on the orientation of the interface. For a fixed orientation this periodic structure "melts" as ve is increased. We determine the dynamical "phase-diagram" of this system in the ve-orientation plane.