A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces

TL;DR

This paper reviews 30 years of research on the KPZ equation, highlighting recent advances, experimental aspects, and exploring higher-dimensional and radial variants to deepen understanding of kinetically roughened surfaces.

Contribution

It provides a comprehensive overview of KPZ developments, introduces an expanding substrates formalism for 3D radial KPZ, and examines extremal paths on disordered lattices, extending the theoretical landscape.

Findings

Recent solutions clarify 1+1 KPZ behavior

New formalism accesses 3D radial KPZ dynamics

Exploration of high-dimensional KPZ limits

Abstract

The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we i) pay debts to heroic predecessors, ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of $d$=$\infty$ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.