LOFF the inhomogeneous faces of color superconductivity Marco

LOFF, the inhomogeneous “faces” of color superconductivity Marco Ruggieri Università degli Studi di Bari Conversano, QCD@work 2005, 16 – 20 Giugno 2005

High density QCD n n Hadrons at very high density and low temperature: deconfinement. Degrees of freedom: quarks and gluons. Quarks fill large Fermi surfaces. One gluon exchange is attractive in the color antisymmetric channel. Color Superconductivity 2

BCS color superconductivity Superficie di Fermi Surface BCS: Pairing with zero total momentum 3

BCS color superconductivity 2 n Phases characterized by diquark condensation: Superconductive Normal 4

In nature……… n Fermi momenta of the quarks can be different, different because: n Weak equilibrium n Non-zero masses of the quarks n Electrical and color neutrality How can this affect BCS superconductivity 5?

Different Fermi momenta u u From now on I consider only d two flavor quark matter d It is difficult to form pairs with total zero momentum 6

Pairs with non-zero total momenum Inhomogeneous gap parameter LOFF phase 7

Cristallography of the LOFF phase One can make the following general ansatz: Usually the wave vectors are choosen along the direction of vertices of regular poliedra Cristallography 8

Interesting cristallographic structures P=6 Body centered cube (B. C. C. ) P=8 Face centered cube (F. C. C. ) 9

Smearing of the gap parameter My goal is to see which is the LOFF structure realized in quark matter. I can do this by comparing the free energy of the various structures. Gap equation = How can I compute such a free energy ? Free energy 10

Comparison of the free energies One wave BCC FCC BCS LOFF 11 (Ruggieri et al. - 2004)

LOFF and compact stars ? Mantel + hadron superfluid If quark matter is present in the core of a neutron star, then the LOFF phase could be LOFF, realized there. g. CFL (if densities are high enough) 12

If LOFF, how can it contribuite to thermodynamics ? n Gapless fermion dispersion laws Fermions are relevant for the BCSthermodynamical properties. n n Spatial symmetries are LOFF spontaneously broken Phonons 13

Conlusions and open questions n n n Different Fermi momenta: pairs with non-zero momemtum. Cristallography of the LOFF phase: smearing approximation. LOFF with three flavors. Transport coefficients. Applications to condensed matter. 14

References In this talk I presented results obtained in collaboration with: R. Casalbuoni, M. Ciminale, R. Gatto, M. Mannarelli, G. Nardulli. Thanks to all of them. Thanks also to: V. Laporta, N. Ippolito, John Petrucci and, last but not least, M. La Calamita. 15