Related papers: Periodic and open classical spin Calogero-Moser ch…
The canonical transformation and its unitary counterpart which relate the rational Calogero-Moser system to the free one are constructed.
Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar…
We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…
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…
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…
A convenient algebraic structure to describe some forms of dynamics of two hamiltonian systems with nonpotential (magnetic--type) interaction is considered. An algebraic mechanism of generation of such dynamics is explored on simple "toy"…
Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse,…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and…
We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, as if it were a classical Hamiltonian with a non-standard potential. The trajectories turn out to be closed ellipses. We…
We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection…
We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the…
We construct a new exactly solvable supersymmetric spin chain related to the BC_N extended root system, which includes as a particular case the BC_N version of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin…
The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly…
A generalized effective spin-chain model is developed for studies of strongly interacting spinor gases in a one-dimensional (1D) optical lattice. The spinor gas is mapped to a system of spinless fermions and a spin-chain. A generalized…
A large (infinitely-dimensional) class of completely integrable (possibly non-autonomous) spin chains is discovered associated to an infinite-dimensional Lie Algebra of infinite rank. The complete set of integrals of motion is constructed…
We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $\mathfrak{gl}_N$ XXZ-type spin chain on $M$ sites is isomorphic to a…
We show that the supersymmetric rational Calogero-Moser-Sutherland (CMS) model of A_{N+1}-type is equivalent to a set of free super-oscillators, through a similarity transformation. We prescribe methods to construct the complete…
Completely integrable Hamiltonians defining classical mechanical systems of $N$ coupled oscillators are obtained from Poisson realizations of Heisenberg--Weyl, harmonic oscillator and $sl(2,\R)$ coalgebras. Various completely integrable…