相关论文: Rationally extended many-body truncated Calogero-S…
By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose…
A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by…
We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with…
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed…
We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the…
The U(1) Calogero Sutherland Model with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered…
The present article is an extended version of the paper {\it Phys. Rev.} {\bf B 59}, R2490 (1999), where, we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach…
Quantum Calogero-Sutherland model of $A_n$ type is completely integrable. Using this fact, we give an elementary construction of lowering an raising operators for the trigonometric case. This is similar, but more complicated (due to the…
We consider the inequivalent quantizations of a $N$-body rational Calogero model with a Coulomb type interaction. It is shown that for certain range of the coupling constants, this system admits a one-parameter family of self-adjoint…
We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass…
An integrable extension of the Calogero model is proposed to study the competing effect of momentum dependent long-range interaction over the original ${1 \ov r^2}$ interaction. The eigenvalue problem is exactly solved and the consequences…
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…
Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown…
We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these…
A new generalization of the Calogero's rational ($A_N$) many-body quantum model is proposed and studied. The key innovation lies in an asymmetrization of the Calogero's two-body interaction. In the generalized model the exact solvability is…
We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in…
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with…
We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide…
We show that and how PT symmetry (interpreted as a "weakened Hermiticity") can be extended to the exactly solvable two- and three-particle Calogero model.