Ruijsenaars-schneider Models and Their Spectral Curves
ثبت نشده
چکیده
We study the elliptic C n and BC n Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameter-ized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero-Moser and Toda types.
منابع مشابه
Ruijsenaars-Schneider models and their spectral curves
We study the elliptic Cn and BCn Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the syst...
متن کاملOn the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n, C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsen...
متن کامل2 . 1 Model and equations of motion
We study the elliptic C n and BC n Ruijsenaars-Schneider models which is elliptic generalization of system given in [1]. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameter-ized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the s...
متن کاملStructures in Bc N Ruijsenaars-schneider Models
We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...
متن کاملA pr 1 99 6 Elliptic Ruijsenaars – Schneider and Calogero – Moser hierarchies are governed by the same r – matrix
We demonstrate that in a certain gauge the elliptic Ruijsenaars– Schneider models admit Lax representation governed by the same dynamical r– matrix as their non–relativistic counterparts (Calogero–Moser models). This phenomenon was previously observed for the rational and hyperbolic models.
متن کامل