Nonequilibrium cluster diffusion during growth and evaporation in two dimensions.

The diffusion of growing or evaporating two-dimensional clusters is investigated. At equilibrium, it is well known that the mean square displacement (MSD) of the cluster center of mass is linear in time. In nonequilibrium conditions, we find that the MSD exhibits a nonlinear time dependence, leading to three regimes: (i) during curvature-driven evaporation, the MSD shows a square-root singularity close to the collapse time; (ii) in slow growth or evaporation, the dynamics is in the Edwards-Wilkinson universality class, and the MSD shows a logarithmic behavior; (iii) far from equilibrium, the dynamics belongs to the Kardar-Parisi-Zhang universality class and the MSD shows a power-law behavior with a characteristic exponent 1/3. These results agree with kinetic Monte Carlo simulations, and can be generalized to other universality classes.