Stochastic fluctuations far from equilibrium: Statistical mechanics of surface growth

This thesis focuses on theoretical studies of nonequilibrium fluctuations during surface growth.; We first study the skewness of Kardar-Parisi-Zhang (KPZ) type growth in the stationary states to understand the fixed point structure of the KPZ universality class. We show the amplitude ratios between the second, fourth moments and the skewness of the surface height distribution are universal. The universal ratios, $W3/W1.52$ = −0.27 (1) and $W4/W22$ = +3.15 (2), are determined by carefully analysis with finite size scaling corrections. The smaller corrections to scaling for the universal ratio allow us to resolve the discrepancy of the roughness exponent between different realizations of KPZ type surface.; The surface reconstruction order on a growing surface is then investigated. We find a reconstructed order exists only below a crossover length, l_rec. The later behavior would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature the surfaces evolve in a layer-by-layer mode within a crossover length scale l_R, but are always rough at large length scales. We investigate this issue in the context of the KPZ type dynamics. We find that during growth reconstruction order is absent in the thermodynamic limit, but exists below a crossover length l_rec > l _R. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics.; The ridge-line trapped domain walls inspire a novel method to explore the fluctuations of the topological features on growing surfaces. Passive random walker (PRW) dynamics is introduced. The PRW is designed to drift upward or downward and then follow specific topological features, like hill tops or valley bottoms, of the growing surface. The PRW can be used to directly explore scaling properties of otherwise somewhat hidden topological features. The world lines of a set of merging PRWs show nontrivial coalescence behaviors and display the river-like network structures of surface ridges in space-time. In other dynamics, like Edwards-Wilkinson growth, this does not happen. The PRWs in KPZ-type surface growth are closely related to the shock waves in the noiseless Burgers equation.