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

Main Directions and Didactic Principles of Using Multimedia Electronic Resources in a Pedagogical University

Currently, the main attention in the field of informatization of education is focused on the problems of creating and using effective multimedia electronic resources. To achieve the completeness and quality of the use of scientific and practical knowledge in the educational activities of pedagogical institutions, it is necessary to create an effective information support system. The article discusses the main directions and didactic principles of using multimedia electronic resources in the system of teacher education

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

Seiberg-Witten curves and double-elliptic integrable systems

An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical variables and the Seiberg-Witten differential providing the pre-symplectic structure. We describe a number of theta-constant equations needed to prove this conjecture for the $N$-particle system. These equations provide an alternative method to derive the Seiberg-Witten prepotential and we illustrate this by calculating the perturbative contribution. We provide evidence that the solutions to the commutativity equations are exhausted by the double-elliptic system and its degenerations (Calogero and Ruijsenaars systems). Further, the theta-function identities that lie behind the Poisson commutativity of the three-particle Hamiltonians are proven

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

Classical and quantum dynamics of confined test particles in brane gravity

A model is constructed for the confinement of test particles moving on a brane. Within the classical framework of this theory, confining a test particle to the brane eliminates the effects of extra dimensions, rendering them undetectable. However, in the quantized version of the theory, the effects of the gauge fields and extrinsic curvature are pronounced and this might provide a hint for detecting them. As a consequence of confinement the mass of the test particle is shown to be quantized. The condition of stability against small perturbations along extra dimensions is also studied and its relation to dark matter is discussed.Comment: 15 pages, no figures, extended, references adde