Inozemtsev V.I. Integrable Many-particle Systems

World Scientific, 2023. — 267 p.Preface
Classical Systems Disconnected with Lie Algebras
Integrable Models of the Motion of Two Particles Interacting with Particle of Infinite Mass
The Motion of Classical Integrable Particle Systems in an External Field
New Completely Integrable Multiparticle Dynamical Systems
Integrable Particle Systems in an External Field Generated by a Particle of Infinite Mass and Motion of the Poles of the Solutions to Inhomogeneous Burgers–Hopf Equation
Classical Sutherland Systems in the Morse Potential
Elliptic Solutions of Equations of Motion of Two Interacting Particles in an External Field
Matrix Analogs of Elliptic Functions
Extension of the Class of Integrable Dynamical Systems Connected with Semisimple Lie Algebras
The Finite Toda Lattices
Lax Representation with Spectral Parameter on a Torus for Integrable Particle Systems
Quantum Systems
The Ground-State Wave Functions of Calogero–Sutherland Quantum Systems in an External Field
Factorization of the Ground-State Wave Functions of the System of Particles Interacting with Particle of Infinite Mass
Equilibrium Points of Classical Integrable Particle Systems, Factorization of Wave Functions of their Quantum Analogs and Polynomial Solutions of the Hill Equation
The Structure of Eigenvectors of the Multidimensional Lamé Operator
The Discrete Spectrum of New Exactly Solvable Quantum N-body Problem on a Line
Wave Functions of Discrete Spectrum States of Integrable Quantum Systems with N Degrees of Freedom
The Discrete Spectrum of Quantum Systems in the Pöshl–Teller Potential
Integrable Systems of Quasi-particles
Introduction
Lax Pair and Integrability
The Infinite Chain
Two-magnon scattering
Multimagnon scattering
Periodic Boundary Conditions and Bethe Ansatz Equations
Two-magnon scattering
Three-magnon scattering
Multimagnon states
ABA Results for Large N
Inhomogeneous Lattices
The Related Hubbard Chains: Are They Integrable?
Concluding Remarks
Integrable Systems of Particles with Spin
Systems of Particles Interacting via Rational and Trigonometric Potentials
A Special Set of Eigenvectors for the Hyperbolic Sutherland Systems with Spin in the Morse Potential
Toward the Proof of Complete Integrability of Quantum Elliptic Many-Particle Systems with Spin Degrees of Freedom
Solution of Three-Particle Spin Elliptic Calogero–Moser System
References