相关论文: Calogero-Moser models with internal degrees of fre…

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 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 prove the density property for generalized Calogero--Moser spaces with inner degrees of freedom. This allows us to describe the holomorphic automorphism group of these complex affine manifolds. These generalized Calogero--Moser spaces…

The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on…

Dynamic degrees of freedom and internal variables are treated in a uniform way. The unification is achieved by means of the introduction of a dual internal variable. This duality provides the corresponding evolution equations depending on…

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…

Calogero-Moser systems are classical and quantum integrable multi-particle dynamics defined for any root system $\Delta$. The {\em quantum} Calogero systems having $1/q^2$ potential and a confining $q^2$ potential and the Sutherland systems…

Dynamical algebra notion of quantum degrees of freedom is utilized to study the relation between quantum dynamical integrability and generalized entanglement. It is argued that a quantum dynamical system generates generalized entanglement…

We present an elementary discussion of the Calogero-Moser model. This gives us an opportunity to illustrate basic concepts of the dynamical integrable models. Some ideas are also presented regarding interconnections between integrable…

The quantization of many-body systems with balanced loss and gain is investigated. Two types of models characterized by either translational invariance or rotational symmetry under rotation in a pseudo-Euclidean space are considered. A…

We establish the exact correspondence of the Calogero-Marchioro-Wolfes model and several of its generalizations with free oscillators. This connection yields the eigenstates and leads to a proof of the quantum integrability. The usefulness…

In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…

There are at least three different notions of degrees of freedom (DF) that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the…

The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…

Classical Calogero-Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an…

We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…

We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…

A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ -- D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free…

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…