Related papers: Generalized Calogero model in arbitrary dimensions
We review a recent construction of an explicit analytic series representation for symmetric polynomials which up to a groundstate factor are eigenfunctions of Calogero-Sutherland type models. We also indicate a generalisation of this result…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
The 40-year-old Calogero-Sutherland (CS) model remains a source of inspirations for understanding 1d interacting fermions. At $\beta=1, \text{or}0$, the CS model describes a free non-relativistic fermion, or boson theory, while for generic…
We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…
We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed…
On the basis of the collective field method, we analyze the Calogero--Sutherland model (CSM) and the Selberg--Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for…
The Calogero model is an interacting, $N$-particle, $\mathfrak{sl}(2,\mathbb R)$-invariant quantum mechanics, whose Hilbert space is furnished by a tower of discrete series modules. The system enjoys both classical and quantum integrability…
We consider the large-N Calogero model in the \h\ collective-field approach based on the $1/N$ expansion. The Bogomol'nyi limit appears and the corresponding equation for the semiclassical configuration gives the correct ground-state…
We investigate the sub-Planck-scale structures associated with the SU(1,1) group by establishing that the Planck scale on the hyperbolic plane can be considered as the inverse of the Bargmann index $k$. Our discussion involves SU(1,1)…
We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the…
The occurrence of quasi-long-range positional order in the ground-state of the one-dimensional repulsive Calogero-Sutherland model is studied. By mapping the exact ground-state into a one dimensional classical system of interacting…
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…
Generalized coherent states are developed for SU(n) systems for arbitrary $n$. This is done by first iteratively determining explicit representations for the SU(n) coherent states, and then determining parametric representations useful for…
We briefly review some recent results concerning algebraical (oscillator) aspects of the $N$-body single-species and multispecies Calogero models in one dimension. We show how these models emerge from the matrix generalization of the…
We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional $1/r^2$ interaction model). In particular, it is shown that…
We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the…
We study the dynamical symmetry algebra of the N-body Calogero model describing the structure of degenerate levels and demonstrate that the algebra is intrisically polynomial. We discuss some general properties of an algebra of…
We introduce a generalization structure of the su(1,1) algebra which depends on a function of one generator of the algebra, f(H). Following the same ideas developed to the generalized Heisenberg algebra (GHA) and to the generalized su(2),…
The quantum-mechanical many-body system with the potential proportional to the pairwise inverse-square distance possesses a strong-weak coupling duality. Based on this duality, particle and/or quasiparticle states are described as SU(1,1)…
The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square interactions. At interaction strength $\lambda=2$, the CSM exhibits a deep connection to anyon…