相关论文: Supersymmetric Extensions of Calogero--Moser--Suth…

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 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…

The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the…

We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the…

The ultraviolet structure of the Calogero-Sutherland models is examined, and, in particular, semions result to have special properties. An analogy with ultraviolet structures known in anyon quantum mechanics is drawn, and it is used to…

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More…

Motivated by topological bidimensional quantum models for distinguishable particles, and by Haldane's definition of mutual statistics for different species of particles, we propose a new class of one-dimensional $1/r_{ij}^2$ Calogero model…

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a model involving many unitary matrices. The resulting systems consist of particles on the circle with internal degrees of freedom, coupled…

We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.

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…

We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…

We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an…

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield…

In this note we analyse two different models of two interacting conformal Carroll particles that can be obtained as the Carrollian limit of two relativistic conformal particles. The first model describes particles with zero velocity and…

The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the…

In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…

Calogero-Sutherland models of $N$ identical particles on a circle are deformed away from hermiticity but retaining a $\cal PT$ symmetry. The interaction potential gets completely regularized, which adds to the energy spectrum an infinite…

In this work, we study a continuous quantum system of a mixture of bosons and fermions with the supersymmetry SU(m|n). The particles are confined in a harmonic well and interact with each other through the 1/r2 interaction. The ground state…

We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…