Abrikosov Gluon Vortices in Color Superconductors

In this talk I will discuss how the in-medium magnetic field can influence the gluon dynamics in a three-flavor color superconductor. It will be shown how at field strengths comparable to the charged gluon Meissner mass a new phase can be realized, giving rise to Abrikosov's vortices of charged gluons. In that phase, the inhomogeneous gluon condensate anti-screens the magnetic field due to the anomalous magnetic moment of these spin-1 particles. This paramagnetic effect can be of interest for astrophysics, since due to the gluon vortex antiscreening mechanism, compact stars with color superconducting cores could have larger magnetic fields than neutron stars made up entirely of nuclear matter. I will also discuss a second gluon condensation phenomenon connected to the Meissner instability attained at moderate densities by two-flavor color superconductors. In this situation, an inhomogeneous condensate of charged gluons emerges to remove the chromomagnetic instability created by the pairing mismatch, and as a consequence, the charged gluonic currents induce a magnetic field. Finally, I will point out a possible relation between glitches in neutron stars and the existence of the gluon vortices.Comment: Talk given at XII Mexican Workshop on Particles & Fields. Mazatlan, Sinaloa, Mexico, Nov.200

Exact Kohn-Sham eigenstates versus quasiparticles in simple models of strongly correlated electrons

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion models. The exact exchange and correlation potentials are fully non-local. The analytic expressions allow to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasi-particle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the non-trivial features of the many-body quasi-particle spectrum, as for example the precursors of the Kondo peak. However, we find that some pieces of the quasi-particle spectrum are missing because the many-body phase-space for electron and hole excitations is richer