On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.Comment: Based on talk at the workshop CQIS-2011 (Protvino, Russia, January 2011), 12 page

Hamiltonian reductions of free particles under polar actions of compact Lie groups

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.Comment: 15 pages, minor correction and updated references in v

Motion of a Particle with Isospin in the Presence of a Monopole

From a consistent expression for the quadriforce describing the interaction between a coloured particle and gauge fields, we investigate the relativistic motion of a particle with isospin interacting with a BPS monopole and with a Julia-Zee dyon. The analysis of such systems reveals the existence of unidimensional unbounded motion and asymptotic trajectories restricted to conical surfaces, which resembles the equivalent case of Electromagnetism.Comment: 10 pages, 2 figures, onecolum

On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsenaars using direct methods, can be then interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex

Effect of magnesium doping on the orbital and magnetic order in LiNiO2

In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and electron spin resonance (ESR), we show that magnesium doping does not stabilize any magnetic or orbital order, despite the absence of interplane Ni2+. A disordered, slowly fluctuating state develops below 12 K. In addition, we find that magnons are excited on the time scale of the ESR experiment. At the same time, a g factor anisotropy is observed, in agreement with $| 3z^{2}-r^{2}>$ orbital occupancy

On the scattering theory of the classical hyperbolic C(n) Sutherland model

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

Self-Field Effects in Magneto-Thermal Instabilities for Nb-Sn Strands

Recent advancements in the critical current density (Jc) of Nb$_{3}$Sn conductors, coupled with a large effective filament size, have drawn attention to the problem of magnetothermal instabilities. At low magnetic fields, the quench current of such high Jc Nb$_{3}$Sn strands is significantly lower than their critical current because of the above-mentioned instabilities. An adiabatic model to calculate the minimum current at which a strand can quench due to magneto-thermal instabilities is developed. The model is based on an 'integral' approach already used elsewhere [1]. The main difference with respect to the previous model is the addition of the self-field effect that allows to describe premature quenches of non-magnetized Nb$_{3}$Sn strands and to better calculate the quench current of strongly magnetized strands. The model is in good agreement with experimental results at 4.2 K obtained at Fermilab using virgin Modified Jelly Roll (MJR) strands with a low Residual Resistivity Ratio (RRR) of the stabilizing copper. The prediction of the model at 1.9 K and the results of the tests carried out at CERN, at 4.2 K and 1.9 K, on a 0.8 mm Rod Re-Stack Process (RRP) strand with a low RRR value are discussed. At 1.9 K the test revealed an unexpected strand performance at low fields that might be a sign of a new stability regime