Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9908045 · Physical Review A

Realization of the Calogero-Moser scattering states as coherent states

Nakka Gurappa, Priti S. Mohanty, Prasanta Kumar Panigrahi

Published Feb 15, 2000• 9 citations
arXivHTMLPDF

Abstract

A realization is provided for the scattering states of the N-particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic treatment is straightforwardly extendable to a large number of few- and many-body interacting systems in one and higher dimensions.

DOI
10.1103/physreva.61.034703

Related papers

Singular factorizations, self-adjoint extensions and applications to quantum many-body physics

Edwin Langmann A, Ari Arievich Laptev, Cornelius Paufler

We study self-adjoint operators defined by factorizing second-order differential operators in first-order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum-mechanical models such as the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero–Sutherland type.

arXiv:math-ph/0510046•Journal of Physics A Mathematical and General•Jan 18, 2006•3 citations

N Fermion Ground State of Calogero-Sutherland type Models in Two and Higher Dimensions

Avinash Khare

I obtain the exact ground state of N-fermions in D-dimensions (D ≥ 2) in case the N particles are interacting via long-ranged two-body and three-body interactions and further they are also interacting via the harmonic oscillator potential. I also obtain the N-fermion ground state in case the oscillator potential is replaced by an N-body Coulomb-like interaction.

•Jan 1, 1998•5 citations

Algebraic study of quantum many-body systems with nearest and next-to-nearest neighbour long-range interactions

Meripeni Ezung, Avinash Khare, Prasanta Kumar Panigrahi

The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is mapped to decoupled oscillators; using this connection we establish an equivalent of the Stanley-Macdonald conjecture in the present case. Further, we show that the scattering states can be realized as coherent states. As in the Calogero case, the scattering scenario in our case yields that the initial momenta, {ki}, go over to the final momenta, {k ′ i = kN+1−i}, with energy independent phase shift. We also establish the unitary equivalence of the scattering Hamiltonian to free particles. Finally, we analyse both the AN−1 and BCN models on circle and construct a number of eigenfunctions by making

•Nov 19, 2012•0 citations

Spectrum ofBN-Type Calogero-Sutherland-Moser Model

Takashi Yamamoto

We explicitly construct the excited-state and derive the spectrum of the quantum Calogero-Sutherland-Moser model associated with the Weyl group B N . We also discuss the asymptotic Bethe-ansatz method for this model.

Journal of the Physical Society of Japan•Apr 15, 1994•14 citations

Quantum many-body systems with nearest and next-to-nearest neighbor long-range interactions

Meripeni Ezung, Nakka Gurappa, Avinash Khare +1 more

The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is connected to decoupled oscillators. The analytically obtainable eigenstates are smaller in number as compared to the Calogero-Sutherland family, indicating the quasiexactly solvable nature of these models. The exactly found scattering states, a smaller set as compared to the Calogero case, can be realized as coherent states. The relation of the scattering Hamiltonian to free particles is also established algebraically. We analyze both ${A}_{N\ensuremath{-}1}$ and $B{C}_{N}$ models on a circle and construct a part of the excitation spectrum by making use of the symmetry arguments.

Physical Review B•Mar 22, 2005•15 citations

Unified algebraic approach to few- and many-body correlated systems

Nakka Gurappa, Prasanta Kumar Panigrahi

The present paper is an extended version of another paper [Phys. Rev. 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 for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few- and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain an expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground state and point out the natural emergence of the underlying linear ${W}_{1+\ensuremath{\infty}}$ symmetry in this approach.

arXiv:cond-mat/0302361•Physical review. B, Condensed matter•Apr 30, 2003•13 citations
A realization is provided for the scattering states of the N-particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic treatment is straightforwardly extendable to a large number of few- and many-body interacting systems in one and higher dimensions.
We study self-adjoint operators defined by factorizing second-order differential operators in first-order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum-mechanical models such as the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero–Sutherland type.
The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is mapped to decoupled oscillators; using this connection we establish an equivalent of the Stanley-Macdonald conjecture in the present case. Further, we show that the scattering states can be realized as coherent states. As in the Calogero case, the scattering scenario in our case yields that the initial momenta, {ki}, go over to the final momenta, {k ′ i = kN+1−i}, with energy independent phase shift. We also establish the unitary equivalence of the scattering Hamiltonian to free particles. Finally, we analyse both the AN−1 and BCN models on circle and construct a number of eigenfunctions by making
The bound and scattering states of the many-body systems, related to the short-range Dyson model, are studied. The Hamiltonian for the full-line problem is connected to decoupled oscillators. The analytically obtainable eigenstates are smaller in number as compared to the Calogero-Sutherland family, indicating the quasiexactly solvable nature of these models. The exactly found scattering states, a smaller set as compared to the Calogero case, can be realized as coherent states. The relation of the scattering Hamiltonian to free particles is also established algebraically. We analyze both ${A}_{N\ensuremath{-}1}$ and BCNB{C}_{N}BCN​ models on a circle and construct a part of the excitation spectrum by making use of the symmetry arguments.
The present paper is an extended version of another paper [Phys. Rev. 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 for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few- and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain an expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground state and point out the natural emergence of the underlying linear ${W}_{1+\ensuremath{\infty}}$ symmetry in this approach.