TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.064
TI  - Rapidity distribution within the defocusing non-linear Schrödinger equation model
PY  - 2023/09/26
UR  - https://www.scipost.org/SciPostPhysCore.6.3.064
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 064
A1  - Bezzaz, Yasser
AU  - Dubois, Léa
AU  - Bouchoule, Isabelle
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.064,
	title={{Rapidity distribution within the defocusing non-linear Schrödinger equation model}},
	author={Yasser Bezzaz and Léa Dubois and Isabelle Bouchoule},
	journal={SciPost Phys. Core},
	volume={6},
	pages={064},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.064},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.064},
}