Classical and Quantum Integrability in Laplacian Growth

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.

References in corpus (11)

• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Integrable Structure of Interface Dynamics
• Conformally Invariant Fractals and Potential Theory
• Laplacian Growth and Whitham Equations of Soliton Theory
• Conformal Fractal Geometry and Boundary Quantum Gravity
• Quasi-classical Study of Form Factors in Finite Volume
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• Non-linear WKB Analysis of the String Equation
• New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps
• Remarks on the Whitham equations