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

作者：Takeuchi Kazumasa A^*

来源：Physica A: Statistical Mechanics and Its Applications , 2018, 504: 77-105.

DOI：10.1016/j.physa.2018.03.009

• Kardar-Parisi-Zhang universality class
• Interface growth
• Exact solution
• Tracy-Widom distribution
• Random matrix theory
• Integrable system
• Exclusion process

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.

• 出版日期2018-8-15