The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises

TL;DR

This paper explores the extended applications and recent theoretical advances of the 1+1 dimensional KPZ equation, including its connection to various physical models and the development of the KPZ fixed point.

Contribution

It discusses new applications of the KPZ equation beyond interface growth and introduces the KPZ fixed point as a significant theoretical development.

Findings

Analysis of spin-spin correlations in the Heisenberg chain

Study of equilibrium time-correlations in 1D fluids

Introduction of the KPZ fixed point as a scale-invariant theory

Abstract

In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different physics. Out of a wide choice, the spin-spin time correlations for the Heisenberg chain will be discussed at some length, also the equilibrium time-correlations of the conserved fields for 1D fluids. An interesting recent theoretical advance is the construction of the scale-invariant asymptotic theory, the so-called KPZ fixed point.