New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential

Integrable N-particle systems have an important property that the associated Seiberg-Witten prepotentials satisfy the WDVV equations. However, this does not apply to the most interesting class of elliptic and double-elliptic systems. Studying the commutativity conjecture for theta-functions on the families of associated spectral curves, we derive some other non-linear equations for the perturbative Seiberg-Witten prepotential, which turn out to have exactly the double-elliptic system as their generic solution. In contrast with the WDVV equations, the new equations acquire non-perturbative corrections which are straightforwardly deducible from the commutativity conditions. We obtain such corrections in the first non-trivial case of N=3 and describe the structure of non-perturbative solutions as expansions in powers of the flat moduli with coefficients that are (quasi)modular forms of the elliptic parameter.Comment: 25 page

Rational Top and its Classical R-matrix

We construct a rational integrable system (the rational top) on a coadjoint orbit of ${\rm SL}_N$ Lie group. It is described by the Lax operator with spectral parameter and classical non-dynamical skew-symmetric $r$-matrix. In the case of the orbit of minimal dimension the model is gauge equivalent to the rational Calogero-Moser (CM) system. To obtain the results we represent the Lax operator of the CM model in two different factorized forms -- without spectral parameter (related to spinless case) and another one with the spectral parameter. The latter gives rise to the rational top while the first one is related to generalized Cremmer-Gervais $r$-matrices. The gauge transformation relating the rational top and CM model provides a classical rational version of the IRF-Vertex correspondence. From a geometrical point of view it describes the modification of ${\rm SL}(N,\mathbb C)$-bundles over degenerated elliptic curve. In view of Symplectic Hecke Correspondence the rational top is related to the rational spin CM model. Possible applications and generalizations of the suggested construction are discussed. In particular, the obtained $r$-matrix defines a class of KZB equations.Comment: 19 page

On the hyperfine interaction in rare-earth Van Vleck paramagnets at high magnetic fields

An influence of high magnetic fields on hyperfine interaction in the rare-earth ions with non-magnetic ground state (Van Vleck ions) is theoretically investigated for the case of $Tm^{3+}$ ion in axial symmetrical crystal electric field (ethylsulphate crystal). It is shown that magnetic-field induced distortions of $4f$-electron shell lead to essential changes in hyperfine magnetic field at the nucleus. The proposed theoretical model is in agreement with recent experimental data.Comment: 4 pages, no figures, submitted to J. Phys. : Cond. Mat

A geometric interpretation of the spectral parameter for surfaces of constant mean curvature

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S^3. The application of the Sym formula to this linear problem yields constant mean curvature surfaces in E^3. Independently, we show that the Sym formula itself can be derived by an appropriate limiting process R -> infinity.Comment: 12 page

Elevated systemic antibodies towards commensal gut microbiota in autoinflammatory condition

Article No. e3172Non peer reviewedPublisher PD

Temperature dependence of the EPR linewidth of Yb3+ - ions in Y0.99Yb0.01Ba2Cu3OX compounds: Evidence for an anomaly near TC

Electron paramagnetic resonance experiments on doped Yb3+ ions in YBaCuO compounds with different oxygen contents have been made. We have observed the strong temperature dependence of the EPR linewidth in the all investigated samples caused by the Raman processes of spin-lattice relaxation. The spin-lattice relaxation rate anomaly revealed near TC in the superconducting species can be assigned to the phonon density spectrum changesComment: 10 pages, 4 figures Renewed versio

Role of the mean curvature in the geometry of magnetic confinement configurations

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curvature are optimum for plasma confinement in multimirror open confinement systems and rippled tori.Comment: PDFLaTeX, 10 pages, 5 figure

Stabilization of test particles in Induced Matter Kaluza-Klein theory

The stability conditions for the motion of classical test particles in an $n$-dimensional Induced Matter Kaluza-Klein theory is studied. We show that stabilization requires a variance of the strong energy condition for the induced matter to hold and that it is related to the hierarchy problem. Stabilization of test particles in a FRW universe is also discussed.Comment: 15 pages, 1 figure, to appear in Class. Quantum Gra