An appetizer to modern developments on the Kardar–Parisi–Zhang universality class

Kazumasa A. Takeuchi

Physica A: Statistical Mechanics and its Applications, 2018, vol. 504, issue C, 77-105

Abstract: The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our understanding of the one-dimensional KPZ class has been completely renewed by mathematical physics approaches based on exact solutions. Mathematical physics has played a central role since then, leading to a myriad of new developments, but their implications are clearly not limited to mathematics — as a matter of fact, it can also be studied experimentally. The aim of these lecture notes is to provide an introduction to the field that is accessible to non-specialists, reviewing basic properties of the KPZ class and highlighting main physical outcomes of mathematical developments since the year 2000. It is written in a brief and self-contained manner, with emphasis put on physical intuitions and implications, while only a small (and mostly not the latest) fraction of mathematical developments could be covered. Liquid-crystal experiments by the author and coworkers are also reviewed.

Keywords: Kardar–Parisi–Zhang universality class; Interface growth; Exact solution; Tracy–Widom distribution; Random matrix theory; Integrable system; Exclusion process (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:504:y:2018:i:c:p:77-105

DOI: 10.1016/j.physa.2018.03.009

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