Classical and Quantum Integrability in Laplacian Growth

2015/06/04 by Eldad Bettelheim, Bettelheim, Eldad
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Pattern Formation and Solitons (nlin.PS) #Soft Condensed Matter (cond-mat.soft) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #math-ph #math.MP #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1506.01463

arxiv created 2015/06/04 · openalex publication_date 2015/06/04 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quasi-classical Study of Form Factors in Finite Volume
• Field theoretical construction of an infinite set of quantum commuting operators related with soliton equations

Related

• Quantized Laplacian growth, I: Statistical theory of Laplacian growth
• Quantization of Lax integrable systems and Conformal Field Theory
• Unifying structures in quantum integrable systems
• Reflections
• Studies in Integrable Quantum Lattice Models and Classical Hierarchies