A System of n=3 Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion

The properties of a system of n = 3 coupled oscillators with linear terms in the velocities (magnetic terms) depending in two parameters are studied. We proved the existence of a bi-Hamiltonian structure arising from a non-symplectic symmetry, as well the existence of master symmetries and additional integrals of motion (weak superintegrability) for certain particular values of the parameters.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The Tremblay-Turbiner-Winternitz system on spherical and hyperbolic spaces : Superintegrability, curvature-dependent formalism and complex factorization

The higher-order superintegrability of the Tremblay-Turbiner-Winternitz system (related to the harmonic oscillator) is studied on the two-dimensional spherical and hiperbolic spaces, S_\k^2 (\k>0), and H_{\k}^2 (\k<0). The curvature $\kappa$ is considered as a parameter and all the results are formulated in explicit dependence of $\kappa$. The idea is that the additional constant of motion can be factorized as the product of powers of two particular rather simple complex functions (here denoted by $M_r$ and $N_\phi$). This technique leads to a proof of the superintegrability of the Tremblay-Turbiner-Winternitz system on S_\k^2 (\k>0) and H_{\k}^2 (\k<0), and to the explicit expression of the constants of motion.Comment: one figur

Photon Self-Energy in a Color Superconductor

In a color superconductor the diquark condensates break spontaneously both the color and ordinary electromagnetism, leaving a remanining rotated U(1) symmetry unbroken. The gauge interactions associated to this rotated symmetry may be considered as the in-medium electromagnetism. We compute the in-medium photon self-energy in the presence of diquark condensates at high baryonic density and weak coupling. This is done to one-loop order for the cases of two and three quark flavors. For vanishing temperature, a detailed discussion is given of the low momentum behavior of the photon polarization tensor. A simple physical picture for the propagation of light in color superconducting media is obtained. The main new effect is due to the diquark condensates, which lead to a strong dielectric constant of the medium. The magnetic permeability remains unchanged, because the primary condensates have vanishing spin and angular momentum. In the two flavor case, an additional contribution arises due to gapless quarks and electrons, which is responsible for Debye screening effects. We also discuss the low energy effective theory for the three flavor case in the presence of electromagnetic interactions.Comment: 26 pages, 4 postscript figures, appendix added, to appear in PR

Deriving effective transport equations for non-Abelian plasmas

Within classical transport theory, an approach is presented to derive systematically effective collision terms and noise sources for effective kinetic equations of non-Abelian plasmas. This procedure amounts to the `integrating-out' of fluctuations, and is applicable for in- and out-of-equilibrium situations. When applied to a hot non-Abelian plasma close to equilibrium we recover the collision integral and the noise source first obtained by B\"odeker. It is also shown that our approach, and hence B\"odeker's effective theory, is consistent with the fluctuation-dissipation theorem.Comment: 7 pages, needs sprocl.sty, invited talk given by DFL at 5th workshop on QCD (QCD2000), Villefranche-sur-Mer, France, 3-7 Jan 200

Review of Structural Adjustment in the Philippines

This article has been delivered during the Central Bank Diamond Jubilee celebration on November 21,1988. It reviews the issues of Philippine structural adjustments with a focus on the identification of elements in the past Philippine efforts that appear to be critical in the future adjustment endeavor. It also discusses the problems and the potentials of policy-based lending in support of future structural adjustment efforts in the Philippines.tax structure, agrarian reform, liberalization, structural adjustment, balance of payments, structural reforms, policy adjustment, industrialization