Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

TLDR

Kinetic interfaces form the basis of an interdisciplinary branch of statistical mechanics, where diverse stochastic growth processes are unified by a nonlinear stochastic partial differential equation, yet many open questions remain. The review aims to highlight the intrinsic links between interface growth equations and directed polymer models, and to persuade readers that multidisciplinary statistical mechanics offers a challenging and enjoyable pursuit of surprising depth. The authors present an unorthodox account of the field, concentrating on the interface growth equations and their directed polymer counterparts.

Abstract

Kinetic interfaces form the basis of a fascinating, interdisciplinary branch of statistical mechanics. Diverse stochastic growth processes can be unified via an intriguing nonlinear stochastic partial differential equation whose consequences and generalizations have mobilized a sizeable community of physicists concerned with a statistical description of kinetically roughened surfaces. Substantial analytical, experimental and numerical effort has already been expended. Despite impressive successes, however, there remain many open questions, with much richness and subtlety still to be revealed. In this review, we give an unorthodox account of this rapidly growing field, concentrating on two main lines — the interface growth equations themselves, and their directed polymer counterparts. We emphasize the intrinsic links among the topics discussed, as well as the relationships to other branches of natural science. Our aim is to persuade the reader that multidisciplinary statistical mechanics can be challenging, enjoyable pursuit of surprising depth.