The perturbation of the quantum Calogero-Moser-Sutherland system and related results

Abstract

The Hamiltonian of the trigonometric Calogero-Sutherland model coincides with some limit of the Hamiltonian of the elliptic Calogero-Moser model. In other words the elliptic Hamiltonian is a perturbed operator of the trigonometric one. In this article we show the essential self-adjointness of the Hamiltonian of the elliptic Calogero-Moser model and the regularity (convergence) of the perturbation for the arbitrary root system. We also show the holomorphy of the joint eigenfunctions of the commuting Hamiltonians w.r.t the variables (x_1, >..., x_N) for the A_{N-1}-case. As a result, the algebraic calculation of the perturbation is justified.

Revised version, 35 pages

References in corpus (2)

• Anyons and the elliptic Calogero-Sutherland model
• On the eigenstates of the elliptic Calogero-Moser model

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• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Heun equation and Inozemtsev models
• Series Solutions of the Non-Stationary Heun Equation
• On eigenvalues of Lamé operator
• A method to derive explicit formulas for an elliptic generalization of the Jack polynomials
• On the solutions of multicomponent generalizations of the Lam{é} equation
• On the Inozemtsev model
• Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system
• Towards Finite-Gap Integration of the Inozemtsev Model
• Quasi-exact solvability of Inozemtsev models