1. LOFF, the inhomogeneous “faces” of color superconductivity Marco Ruggieri Università degli Studi di Bari Conversano, QCD@work2005, 16 – 20 Giugno 2005

2. 2 High density QCD 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

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

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

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

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

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

8. 8 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

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

10. 10 Smearing of the gap parameter Gap equation = Free energy 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. How can I compute such a free energy ?

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

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

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

14. 14 Conlusions and open questions 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.

15. 15 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.