Affiliation:
1. Laboratoire Charles Fabry
Abstract
We consider the classical field integrable system whose evolution equation is the nonlinear Schrödinger equation with defocusing non-linearities, which is the classical limit of the quantum Lieb-Liniger model. We propose a simple derivation of the relation between two sets of conserved quantities: on the one hand the trace of the monodromy matrix, parameterized by the spectral parameter and introduced in the inverse-scattering framework, and on the other hand the rapidity distribution, a concept imported from the Lieb-Liniger model. To do so we use the definition of the rapidity distribution as the asymptotic momentum distribution after a very large expansion. We propose two different ways to derive the result, each one using a thought experiment that implements an expansion.
Funder
Agence Nationale de la Recherche
Subject
Statistical and Nonlinear Physics,Atomic and Molecular Physics, and Optics,Nuclear and High Energy Physics,Condensed Matter Physics
Cited by
2 articles.
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