Particle Scattering and Fusion for the Ablowitz-Ladik Chain

Autor:	Brollo, Alberto, Spohn, Herbert
Rok vydání:	2024
Předmět:	Condensed Matter - Statistical Mechanics Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/ad6411
Popis:	The Ablowitz-Ladik chain is an integrable discretized version of the nonlinear Schr\"{o}dinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with $1/\sinh^2$ pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the Ablowitz-Ladik chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule. Comment: 32 pages, 5 figures, 2 appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.07095 Zobrazit plný text záznamu View this record from Arxiv