相关论文: Two body systems from sl(2,C)-tops

We analyze a generalization of the quantum Calogero model with the underlying conformal symmetry, paying special attention to the two-body model deformation. Owing to the underlying $ SU(1,1) $ symmetry, we find that the analytic solutions…

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…

We prove that any two algebraic embeddings of $\mathbb{C}$ into $\textrm{SL}_n(\mathbb{C})$ are the same up to an algebraic automorphism of $\textrm{SL}_n(\mathbb{C})$, provided that $n$ is at least $3$. Moreover, we prove that two…

In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian…

We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in $N$ components and its associated system of conservation laws is in bijective correspondence with an alternating three-form on a $N+2$-dimensional…

For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a general procedure for constructing Baecklund transformation is proposed. The…

We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is an integrable Euler-Arnold top on the complex group GL(N) for any $N$, whose inertia ellipsiod is related to a choice…

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…

Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are canonically isomorphic. We discuss how this conjecture can be approached by means of…

General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a…

In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models.…

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…

Non-Hermitian but ${\cal PT}-$symmetric quantum system of an $N-$plet of bosons described by the three-parametric Bose-Hubbard Hamiltonian $H(\gamma,v,c)$ is picked up, in its special exceptional-point limit $c \to 0$ and $\gamma \to v$, as…

Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a $\nu$-deformation…

An overview of maximally superintegrable classical Hamitonians on spherically symmetric spaces is presented. It turns out that each of these systems can be considered either as an oscillator or as a Kepler-Coulomb Hamiltonian. We show that…

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out.…

We investigate the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is invariant under the field transformation which reduces the non-linear Dirac brackets of…

Given an irreducible unitary representation of a cocompact lattice of SL(2,C), we explicitly write down a solution of the Strominger system of equations. These solutions satisfy the equation of motion, and the underlying holomorphic vector…

We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…

We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification…