Integrable fishnet circuits and Brownian solitons
Statistical Mechanics
2025-07-23 v4 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a `fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion.
Cite
@article{arxiv.2411.08030,
title = {Integrable fishnet circuits and Brownian solitons},
author = {Žiga Krajnik and Enej Ilievski and Tomaž Prosen and Benjamin J. A. Héry and Vincent Pasquier},
journal= {arXiv preprint arXiv:2411.08030},
year = {2025}
}
Comments
v3: added missing references, v4 minor clarifications