Integrable deformations of oscillator chains from quantum algebras

Angel Ballesteros; Francisco J. Herranz

doi:10.1088/0305-4470/32/50/306

Home/Archive/arXiv

arXiv · solv-int/9911004

Integrable deformations of oscillator chains from quantum algebras

Angel Ballesteros·Francisco J. Herranz

View original source ↗Read source document ↗Export metadata ↓

Abstract

A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion are given, and the long-range nature of the interactions introduced by the deformation is shown to be linked to the underlying coalgebra structure. Separability and superintegrability properties of such systems are analysed, and their connection with classical angular momentum chains is used to construct a non-standard integrable deformation of the XXX hyperbolic Gaudin system.

Explore related subjects

solv-int math.QA nlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Angel Ballesteros, Francisco J. Herranz. 1999-11-03. Integrable deformations of oscillator chains from quantum algebras. https://doi.org/10.1088/0305-4470%2F32%2F50%2F306

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2024

Integer spin particles necessarily produce half-integer angular momentum in a simple complex and periodic Hamiltonian

Exact wave functions are is derived from an azimuthally periodic a self-consistent quantum Hamiltonian in 2+1 dimensions using both the Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for both relativistic and non-relativistic equations, integer spin wave equations necessarily produce half-integer angular momentum in this potential. We find additionally that the higher energy, relativistic, solutions require an asymptotically free potential, while the lower energy, Schroedinger, solutions can exist in a potential that grows linearly with r. These are purely mathematical results, however we speculate on possible physical interpretations.

solv-int↗

arXiv2017

The averaging of non-local Hamiltonian structures in Whitham's method

We consider the $m$-phase Whitham's averaging method and propose a procedure of "averaging" of non-local Hamiltonian structures. The procedure is based on the existence of a sufficient number of local commuting integrals of a system and gives a Poisson bracket of Ferapontov type for the Whitham's system. The method can be considered as a generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets.

solv-int↗

arXiv2013

On two aspects of the Painleve analysis

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Backlund transformation related to the Lax pair.

solv-int↗