Particle scattering and fusion for the Ablowitz-Ladik chain

Alberto Brollo, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

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Abstract

The Ablowitz-Ladik (AL) chain is an integrable discretized version of the nonlinear Schrödinger 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 AL 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.

Original languageEnglish
Article number325202
JournalJournal of Physics A: Mathematical and Theoretical
Volume57
Issue number32
DOIs
StatePublished - 9 Aug 2024

Keywords

  • Ablowitz-Ladik chain
  • classical integrable systems
  • classical spin chains
  • generalized Gibbs free energy
  • scattering theory

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