Quantum Group Symmetry of Integrable Systems With or Without Boundary

Ragoucy, É.

doi:10.1142/s0217751x02010819

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…The explicit realization of this relationship is the main goal of this investigation. Our analysis extends the results of [13,14], obtained in the case of pure reflection. Establishing the link between ZF and RT algebras, we take the occasion to discuss also the issue of symmetries when impurities are present.…”

Section: Introductionsupporting

confidence: 89%

Interplay between Zamolodchikov–Faddeev and reflection–transmission algebras

Mintchev¹,

Ragoucy²

2003

J. Phys. A: Math. Gen.

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Section: Introductionsupporting

confidence: 89%

Interplay between Zamolodchikov–Faddeev and reflection–transmission algebras

Mintchev¹,

Ragoucy²

2003

J. Phys. A: Math. Gen.

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“…On the other hand the advantage of this approach is the possibility of generalizing it to other specific boundary or initial conditions. In principle this formalism should allow one to include impurities [38] and can be extended to multi-component generalizations of the NSE [39].…”

Section: The Quantum Inverse Scattering Methodsmentioning

confidence: 99%

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

2010

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In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate of particles in a state with zero momentum and a condensate of particles in a gaussian wavepacket in real space. Combining the form-factor approach with the method of intertwining operator we develop a numerical procedure which allows explicit summation over intermediate states and analysis of the time evolution of non-local density-density correlation functions. In both cases we observe a tendency toward formation of crystal-like correlations at intermediate time scales.

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Integrable Systems With Impurity

Ragoucy

2004

Lie Theory and Its Applications in Physics V

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Abstract:After reviewing some basic properties of RT algebras, which appear to be the natural framework to deal with integrable systems in presence of an impurity, we show how any integrable system (including these possessing translation invariance) can be promoted to an integrable system with an impurity which can reflect and transmit particles. The technics allows bulk translation invariant S-matrices while avoiding the no-go theorem stated recently about these laters.

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Quantum Group Symmetry of Integrable Systems With or Without Boundary

Cited by 3 publications

References 19 publications

Interplay between Zamolodchikov–Faddeev and reflection–transmission algebras

Interplay between Zamolodchikov–Faddeev and reflection–transmission algebras

Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas

Integrable Systems With Impurity

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