On the Integrability of Classical Ruijsenaars-Schneider Model of BC2BC_{2} Type

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure

On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange

It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with $N$ sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector of the Hilbert space with magnetization $N/2-M$, $1<M\leq[N/2]$, by means of double quasiperiodic meromorphic solutions to the $M$-particle quantum Calogero-Moser problem on a line. The spectrum and highest-weight states are determined by the solutions of the systems of transcendental equations of the Bethe-ansatz type which arise as restrictions to particle pseudomomenta.Comment: 9 pages, Late

On the two-magnon bound states for the quantum Heisenberg chain with variable range exchange

The spectrum of finite-difference two-magnon operator is investigated for quantum S=1/2 chain with variable range exchange of the form $h(j-k)\propto \sinh^{-2}a(j-k)$. It is found that usual bound state appears for some values of the total pseudomomentum of two magnons as for the Heisenberg chain with nearest-neighbor spin interaction. Besides this state, a new type of bound state with oscillating wave function appears at larger values of the total pseudomomentum.Comment: 8 pages, latex, no figure

New Family of Solvable 1D Heisenberg Models

Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/\sinh^2 x$ on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.Comment: 8 pp, LaTeX, ITP-UH-07/9

Communicative and information technologies in music and the possibilities of their implementation in professional activity

При финансовой поддержке Российского гуманитарного научного фонда, проект № 07-06-14162

Dilemmas of Russia's modernization

Социологический анализ проблем и перспектив модернизации российского общества

Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond

We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics, we derive so called maximal-ranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. These diagrams require proper regularization of not only ultraviolet but also infrared divergences. We first consider standard operator mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and spectrum of the quantum dilatation generator up to six loop orders. We show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N=4 super Yang-Mills theory. We then study spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six loop diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by Ferguson, Baily and Arno.Comment: 1+39 pages, 12 figures, references added, minor structural changes, typos correcte