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Integrability and algebraic structure of the quantum Calogero-Moser model

Miki Wadati, Kazuhiro Hikami, Hideaki Ujino

Chaos Solitons & FractalsNov 1, 19939 citations

Integral representation for the eigenstates of the spin system with inverse square interactions

Kazuhiro Hikami

We consider the Calogero-Sutherland-Moser system with spin - 1/2 . We give the integral representation for the ground state wavefunction. Excited states of the Calogero spin model confined in the harmonic potential are also given.

Journal of Physics A Mathematical and GeneralAug 7, 19949 citations

Quantum Calogero-Moser Model and its Algebraic Structures (統計物理学の展開と応用--多様性の中の類似性(研究会報告))

Miki Wadati, Hideaki Ujino, Kazuhiro Hikami

物性研究Jul 20, 19931 citation

Hierarchies of spin models related to Calogero–Moser models

V. I. Inozemtsev, Ryu Sasaki B

arXiv:hep-th/0105197Nuclear Physics BDec 1, 20014 citations

Towards the proof of complete integrability of quantum elliptic many-body systems with spin degrees of freedom

J. Dittrich, V. I. Inozemtsev

We consider the problem of finding integrals of motion for quantum elliptic Calogero-Moser systems with arbitrary number of particles extended by introducing spinexchange interaction. By direct calculation, after making certain ansatz, we found first two integrals — quite probably, lowest nontrivial members of the whole commutative ring. This result might be considered as the first step in constructing this ring of the operators which commute with the Hamiltonian of the model.

Regular and Chaotic DynamicsApr 1, 20092 citations

Integrability Aspects of the Current Algebra Representation and the Factorized Quantum Nonlinear Schrödinger Type Dynamical Systems

Nikolay N. Bogolubov, Dominik Prorok, Anatolij K. Prykarpatski

Abstract In this work we study integrability aspects of the current algebra representation and the factorized quantum nonlinear Schrödinger type dynamical systems, initiated before by G. Goldin with collaborators, in suitably renormalized Fock type Hilbert spaces. There is developed the current algebra representation scheme of reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space. There is presented its application to constructing quantum factorized Hamiltonian systems and their symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially one-dimensional models as the Calogero–Moser–Sutherland and Nonlinear Schrödinger dynamical systems of spin-less Bose-particles.Abstract In this work we study integrability aspects of the current algebra representation and the factorized quantum nonlinear Schrödinger type dynamical systems, initiated before by G. Goldin with collaborators, in suitably renormalized Fock type Hilbert spaces. There is developed the current algebra representation scheme of reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space. There is presented its application to constructing quantum factorized Hamiltonian systems and their symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially one-dimensional models as the Calogero–Moser–Sutherland and Nonlinear Schrödinger dynamical systems of spin-less Bose-particles.

Physics of Particles and NucleiJul 1, 20201 citation

Integrability of Calogero-Moser Spin System

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Integrability of Calogero-Moser Spin System

Abstract

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