Integrable Models of Interaction of Matter with Radiation

The simplified models of interaction of charged matter with resonance modes of radiation generalizing the well-known Jaynes-Cummings and Dicke models are considered. It is found that these new models are integrable for arbitrary numbers of dipole sources and resonance modes of the radiation field. The problem of explicit diagonalisation of corresponding Hamiltonians is discussed

Hierarchies of Spin Models related to Calogero-Moser Models

The universal formulation of spin exchange models related to Calogero-Moser models implies the existence of integrable hierarchies, which have not been explored. We show the general structures and features of the spin exchange model hierarchies by taking as examples the well-known Heisenberg spin chain with the nearest neighbour interactions. The energy spectra of the second member of the hierarchy belonging to the models based on the $A_r$ root systems $(r=3,4,5)$ are explicitly and {\em exactly} evaluated. They show many many interesting features and in particular, much higher degree of degeneracy than the original Heisenberg model, as expected from the integrability.Comment: 12pages, LaTeX2e, packages used: pstricks, pst-node, pstcol, if these are not available, an eps file will be sent upon reques

Scalar Symmetries of the Hubbard Models with Variable Range Hopping

Examples of scalar conserved currents are presented for trigonometric, hyperbolic and elliptic versions of the Hubbard model with non-nearest neighbour variable range hopping. They support for the first time the hypothesis about the integrability of the elliptic version. The two- electron wave functions are constructed in an explicit form.Comment: 9 pages, LaTex2e, no figure

On the breakdown of perturbative integrability in large N matrix models

We study the perturbative integrability of the planar sector of a massive SU(N) matrix quantum mechanical theory with global SO(6) invariance and Yang-Mills-like interaction. This model arises as a consistent truncation of maximally supersymmetric Yang-Mills theory on a three-sphere to the lowest modes of the scalar fields. In fact, our studies mimic the current investigations concerning the integrability properties of this gauge theory. Like in the field theory we can prove the planar integrability of the SO(6) model at first perturbative order. At higher orders we restrict ourselves to the widely studied SU(2) subsector spanned by two complexified scalar fields of the theory. We show that our toy model satisfies all commonly studied integrability requirements such as degeneracies in the spectrum, existence of conserved charges and factorized scattering up to third perturbative order. These are the same qualitative features as the ones found in super Yang-Mills theory, which were enough to conjecture the all-loop integrability of that theory. For the SO(6) model, however, we show that these properties are not sufficient to predict higher loop integrability. In fact, we explicitly demonstrate the breakdown of perturbative integrability at fourth order.Comment: 27 page

On the solutions of multicomponent generalizations of the Lam{\'e} equation

We describe a class of the singular solutions to the multicomponent analogs of the Lam{\'e} equation, arising as equations of motion of the elliptic Calogero--Moser systems of particles carrying spin 1/2. At special value of the coupling constant we propose the ansatz which allows one to get meromorphic solutions with two arbitrary parameters. They are quantized upon the requirement of the regularity of the wave function on the hyperplanes at which particles meet and imposing periodic boundary conditions. We find also the extra integrals of motion for three-particle systems which commute with the Hamiltonian for arbitrary values of the coupling constant.Comment: 8 pages, 1 table, no figures, revtex

Explicit solution of the (quantum) elliptic Calogero-Sutherland model

We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide an elliptic deformation of the Jack polynomials. We prove in certain special cases that these series have a finite radius of convergence in the nome $q$ of the elliptic functions, including the two particle (= Lam\'e) case for non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper completely revised: the results of v1 and v2 are extended to all order

A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills

We probe the long-range spin chain approach to planar N=4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the SU(2) subsector of the state space up to three loops, but ceases to exhibit the conjectured thermodynamic scaling properties at higher orders. We indicate how this may be bypassed while nevertheless preserving integrability, and suggest the corresponding all-loop asymptotic Bethe ansatz. We also propose the local part of the all-loop gauge transfer matrix, leading to conjectures for the asymptotically exact formulae for all local commuting charges. The ansatz is finally shown to be related to a standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical string theory uncovers a detailed, non-perturbative agreement between the corresponding expressions for the infinite tower of local charge densities. However, the respective Bethe equations differ slightly, and we end by refining and elaborating a previously proposed possible explanation for this disagreement.Comment: 48 pages, 1 figure. v2, further results added: discussion of the relationship to an inhomogeneous spin chain, normalization in sec 3 unified, v3: minor mistakes corrected, published versio

The Poisson bracket compatible with the classical reflection equation algebra

We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the reflection equation algebra bracket. Then we use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes the $XXX$ Heisenberg magnet with boundary conditions, the generalized Toda lattices and the Kowalevski top.Comment: 13 pages, LaTeX with AmsFont

ВЛИЯНИЕ ТИМИЧЕСКИХ ПЕПТИДОВ НА АНАЛЬГЕЗИЮ, ВЫЗВАННУЮ ОСТРОЙ И ПОДОСТРОЙ ИММОБИЛИЗАЦИЕЙ

Objective: Our aim was to investigate the influence of thymic polypeptides on pain sensitivity and to analyze a possible role of the opioid system in the implementation of the analgesia caused by immobilization stress. Methods: The study was performed on male Wistar rats at the Moscow state University named after M. V. Lomonosov. We studied effects of thymus peptides: thymuline (0.15 mg/kg), fraction 5 thymosin (0.25 microgram/kg) and tactivin (0.5 mg/kg) on pain sensitivity in rats using test «tail flick» without stress, with acute (3 h) and sub acute (12 h) immobilization stress. The comparison groups were animals treated with saline and spleen polypeptides. Results: It is shown that preparations of thymus increase the threshold of pain sensitivity in the intact animals. Immobilization stress duration 3 and 12 h in thymus peptides treated rats caused a less pronounced increase in pain threshold than in the control groups (immobilization stress 3 h: tactivin — р=0.025, thymuline — р=0.022, fraction 5 thymosin — р=0.033; immobilization stress 12 h: tactivin — р=0.034, thymuline — р=0.027, fraction 5 thymosin — р=0.036.). The opioid receptor blocker naloxone (1 mg/kg) did not completely block the stress-induced analgesia, indicating the presence of both opioid and non-opioid components in this state. In thymus peptides treated rats, opioid component was less pronounced than in the control groups (tactivin — р=0.031, thymuline — р=0.026, fraction 5 thymosin — р=0.029). Conclusion: Pre-activation of the opioid system by the thymus polypeptides leads to an increase in the share of non-opioid component of the stress-induced analgesia and prevents the depletion of the opioid system in immobilization stress. Цель исследования: исследовать влияние полипептидов тимуса на болевую чувствительность и определить роль опиоидной системы в реализации анальгезии, вызванной иммобилизационным стрессом. Методы: исследование выполнено на самцах крыс линии Wistar в Московском государственном университете им. М.В. Ломоносова. Изучено влияние пептидов тимуса: тимулина (0,15 мг/кг), фракции 5 тимозина (0,25 мкг/кг) и тактивина (0,5 мг/кг) на болевую чувствительность крыс с помощью теста отдергивания хвоста без стресса, при остром (3 ч) и подостром (12 ч) иммобилизационном стрессе. В контрольные группы были включены животные, получавшие физиологический раствор и полипептиды селезенки. По окончании тестирования снижали активность опиоидной системы налоксоном. Результаты: показано, что препараты тимуса увеличивают порог болевой чувствительности у интактных животных. Иммобилизационный стресс продолжительностью 3 и 12 ч на фоне пептидов тимуса вызывал менее выраженное увеличение порога болевой чувствительности, чем в контрольных группах (иммобилизация 3 ч: тактивин — р =0,025, тимулин — р =0,022, фракция 5 тимозина — р =0,033; иммобилизация 12 ч: тактивин — р =0,034, тимулин — р =0,027, фракция 5 тимозина — р =0,036). Блокатор опиоидных рецепторов налоксон (1 мг/кг) не полностью блокировал стресс-вызванную анальгезию, что свидетельствовало о наличии как опиоидного, так и неопиодного компонентов данного состояния. На фоне пептидов тимуса опиоидный компонент был менее выражен, чем в контрольных группах (тактивин — р =0,031, тимулин — р =0,026, фракция 5 тимозина — р =0,029). Заключение: предварительная активация опиоидной системы полипептидами тимуса приводит к увеличению доли неопиоидного компонента анальгезии при стрессировании и препятствует истощению опиоидной системы при иммобилизационном стрессе.

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.Comment: 13 REVTeX pages + 5 uuencoded figures, UoU-003059