Classical and Quantum Integrability in Laplacian Growth

TL;DR

This paper explores the relationship between Laplacian growth and integrable systems, proposing a potential link to quantum integrability that could predict fractal patterns in growth clusters.

Contribution

It reviews classical integrability in Laplacian growth and introduces a novel hypothesis connecting quantum integrable systems to these growth phenomena.

Findings

Proposes a possible relation between quantum integrable systems and Laplacian growth.

Suggests that conformal field theory could be used to predict fractal properties.

Highlights the need for further research to confirm the connection.

Abstract

We review here particular aspects of the connection between Laplacian growth problems and classical integrable systems. In addition, we put forth a possible relation between quantum integrable systems and Laplacian growth problems. Such a connection, if confirmed, has the potential to allow for a theoretical prediction of the fractal properties of Laplacian growth clusters, through the representation theory of conformal field theory.