Particle Scattering and Fusion for the Ablowitz-Ladik Chain
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909267124027392 |
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| author | Brollo, Alberto Spohn, Herbert |
| author_facet | Brollo, Alberto Spohn, Herbert |
| contents | The Ablowitz-Ladik 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Particle Scattering and Fusion for the Ablowitz-Ladik Chain Brollo, Alberto Spohn, Herbert Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems The Ablowitz-Ladik 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 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. |
| title | Particle Scattering and Fusion for the Ablowitz-Ladik Chain |
| topic | Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2404.07095 |