TY - JOUR
T1 - Particle scattering and fusion for the Ablowitz-Ladik chain
AU - Brollo, Alberto
AU - Spohn, Herbert
N1 - Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
PY - 2024/8/9
Y1 - 2024/8/9
N2 - 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.
AB - 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.
KW - Ablowitz-Ladik chain
KW - classical integrable systems
KW - classical spin chains
KW - generalized Gibbs free energy
KW - scattering theory
UR - http://www.scopus.com/inward/record.url?scp=85199680577&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ad6411
DO - 10.1088/1751-8121/ad6411
M3 - Article
AN - SCOPUS:85199680577
SN - 1751-8113
VL - 57
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 32
M1 - 325202
ER -