Intriguing similarity between crystal growth and equilibrium facet fluctuations

Abstract

  Crystal growth and equilibrium facet shape fluctuations are different problems in nature, but nontrivial similarity between them was recently argued. On the one hand, recent developments on the Kardar-Parisi-Zhang (KPZ) universality class, which describes surface fluctuations during random domain growth (such as crystal growth), unveiled relevance of random matrix theory in the case of one-dimensional interfaces. In particular, it was shown, both theoretically and experimentally, that the distribution of interface height fluctuations is given by that of the largest eigenvalue of certain random matrices. On the other hand, relation to random matrices was also shown to exist in equilibrium crystals, where positions of step trains correspond to eigenvalues of random matrices, and crystal facet edges to their largest eigenvalues. Remarkably, at least in certain cases, fluctuations of growing interfaces and those of equilibrium facet shapes were theoretically shown to exhibit the same random matrix distribution. Here I outline those two developments, emphasizing how they are connected or not, and discuss some perspectives.