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

SU(1, 1) algebra and interacting families of Calogero particles

Stjepan Meljanac, Marijan Mileković, Anđelo Samsarov, Marko Stojić

Published Jun 24, 2004• 0 citations
OpenAlex

Abstract

A one-dimensional model with F interacting families of Calogero-type particles is studied. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1, 1) structure of the model. We show how SU(1, 1) generators for the whole system are composed of SU(1, 1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants.

Related papers

INTERACTING FAMILIES OF CALOGERO-TYPE PARTICLES AND SU (1,1) ALGEBRA

Stjepan Meljanac, Marijan Mileković, Andjelo Samsarov +1 more

We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU (1,1) structure of the model. We show how SU (1,1) generators for the whole system are composed of SU (1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.

arXiv:hep-th/0405132•Modern Physics Letters B•May 30, 2004•13 citations

Aspects of generalized Calogero model

Stjepan Meljanac, Andjelo Samsarov, Marijan Mileković

A multispecies model of Calogero type in $D\geq 1$ dimensions is constructed. The model includes harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we find the exact eigenenergies corresponding to a class of the exact global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behaviour.

arXiv:hep-th/0411231•Nov 25, 2004•0 citations

Exactly solved quantum many-body systems in one dimension

Martin A. Hallnäs

This thesis is devoted to the study of various examples of exactly solved quantum many-body systems in one-dimension. It is divided into two parts: the first provides background and complementary results to the second, which consists of three scientific papers. The first paper concerns a particu- lar extension, corresponding to the root system CN, of the delta-interaction model. We prove by construction that its exact solution, even in the gen- eral case of distinguishable particles, can be obtained by the coordinate Bethe ansatz. We also elaborate on the physical interpretation of this model. It is well known that the delta-interaction is included in a four parameter family of local interactions. In the second paper we interpret these parameters as cou- pling constants of certain momentum dependent interactions and determine all cases leading to a many-body system of distinguishable particles which can be solved by the coordinate Bethe ansatz. In the third paper we consider the so-called rational Calogero-Sutherland model, describing an arbitrary number of particles on the real line, confined by a harmonic oscillator potential and interacting via a two-body interaction proportional to the inverse square of the inter-particle distance. We construct a novel solution algorithm for this model which enables us to obtain explicit formulas for its eigenfunctions. We also show that our algorithm applies, with minor changes, to all extensions of the rational Calogero-Sutherland model which correspond to a classical root system.

•Jan 1, 2005•0 citations

A multispecies Calogero model

Stjepan Meljanac, Marijan Mileković, Andjelo Samsarov

We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Using an algebraic approach (Fock space analysis), we construct ladder operators and find infinitely many, but not all, exact eigenstates of the model Hamiltonian. Besides the ground state energy, we deduce energies of the excited states. It turns out that the spectrum is linear in quantum numbers and that the higher-energy levels are degenerate. The dynamical symmetry responsible for degeneracy is SU(2). We also find the universal critical point at which the model exhibits singular behaviour. Finally, we make contact with some special cases mentioned in the literature.

arXiv:hep-th/0307126•Physics Letters B•Oct 1, 2003•28 citations

Equivalence of the Calogero-Sutherland model to free harmonic oscillators

Nakka Gurappa, Prasanta Kumar Panigrahi

A similarity transformation is constructed, through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension can be mapped identically to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion, and a linear ${W}_{1+\ensuremath{\infty}}$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.

arXiv:cond-mat/9710035•Physical review. B, Condensed matter•Jan 15, 1999•78 citations

REDUCTION OF ANYONS TO ONE DIMENSION AND CALOGERO–SUTHERLAND-TYPE MODELS

RADHIKA VATHSAN

The two-dimensional anyon system, when reduced to one dimension, yields models related to the Calogero–Sutherland model. One such reduction leads to a new model with a class of exact solutions. This model is one of a family of models obtained upon dimensional reduction of spherically symmetric models in arbitrary dimensions.

arXiv:hep-th/9804137•International Journal of Modern Physics A•Sep 30, 1998•2 citations
A one-dimensional model with F interacting families of Calogero-type particles is studied. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1, 1) structure of the model. We show how SU(1, 1) generators for the whole system are composed of SU(1, 1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants.
We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU (1,1) structure of the model. We show how SU (1,1) generators for the whole system are composed of SU (1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.
A multispecies model of Calogero type in D≥1D\geq 1D≥1 dimensions is constructed. The model includes harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we find the exact eigenenergies corresponding to a class of the exact global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behaviour.
This thesis is devoted to the study of various examples of exactly solved quantum many-body systems in one-dimension. It is divided into two parts: the first provides background and complementary results to the second, which consists of three scientific papers. The first paper concerns a particu- lar extension, corresponding to the root system CN, of the delta-interaction model. We prove by construction that its exact solution, even in the gen- eral case of distinguishable particles, can be obtained by the coordinate Bethe ansatz. We also elaborate on the physical interpretation of this model. It is well known that the delta-interaction is included in a four parameter family of local interactions. In the second paper we interpret these parameters as cou- pling constants of certain momentum dependent interactions and determine all cases leading to a many-body system of distinguishable particles which can be solved by the coordinate Bethe ansatz. In the third paper we consider the so-called rational Calogero-Sutherland model, describing an arbitrary number of particles on the real line, confined by a harmonic oscillator potential and interacting via a two-body interaction proportional to the inverse square of the inter-particle distance. We construct a novel solution algorithm for this model which enables us to obtain explicit formulas for its eigenfunctions. We also show that our algorithm applies, with minor changes, to all extensions of the rational Calogero-Sutherland model which correspond to a classical root system.
We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Using an algebraic approach (Fock space analysis), we construct ladder operators and find infinitely many, but not all, exact eigenstates of the model Hamiltonian. Besides the ground state energy, we deduce energies of the excited states. It turns out that the spectrum is linear in quantum numbers and that the higher-energy levels are degenerate. The dynamical symmetry responsible for degeneracy is SU(2). We also find the universal critical point at which the model exhibits singular behaviour. Finally, we make contact with some special cases mentioned in the literature.
A similarity transformation is constructed, through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension can be mapped identically to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion, and a linear ${W}_{1+\ensuremath{\infty}}$ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.