相关论文: Calogero Models for Distinguishable Particles

We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the…

We construct two different Calogero-Sutherland type models with only two-body interactions in arbitrary dimensions. We obtain some exact wave functions, including the ground states, of these two models for arbitrary number of spinless…

We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics…

We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of…

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…

We solve the N-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$, by constructing annihilation and creation operators of the form $…

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A…

The 3-body Calogero problem is solved by separation of variables for arbitrary exchange statistics. A numerical computation of the 4-body spectrum is also presented. The results display new features in comparison with the standard case of…

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…

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 show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently…

We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type…

We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle…

A coupling-constant definition is given based on the compositeness property of some particle states with respect to the elementary states of other particles. It is applied in the context of the vector-spin-1/2-particle interaction vertices…

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the…

We review some recent results on the Calogero-Sutherland model with emphasis upon its algebraic aspects. We give integral formulae for excited states (Jack polynomials) of this model and their relations with W_n singular vectors and…

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…

A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and…

We show that the N-particle A_{N-1} and B_N rational Calogero models without the harmonic interaction admit a new class of bound and scattering states. These states owe their existence to the self-adjoint extensions of the corresponding…

A generalisation of the classical Calogero-Moser model obtained by coupling it to the Gaudin model is considered. The recently found classical dynamical r-matrix [E. Billey, J. Avan and O. Babelon, PAR LPTHE 93-55] for the…