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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
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
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