LOFF, the inhomogeneous “faces” of color superconductivity

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## LOFF, the inhomogeneous “faces” of color superconductivity

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**LOFF, the inhomogeneous “faces” of color**superconductivity Marco Ruggieri Università degli Studi di Bari Conversano,QCD@work2005, 16 – 20 Giugno 2005**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**Superficie di Fermi**BCS: BCS color superconductivity Fermi Surface Pairing with zero total momentum**Superconductive**Normal BCS color superconductivity 2 • Phases characterized by diquark condensation:**In nature………**• 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 ?**u**u d d It is difficult to form pairs with total zero momentum Different Fermi momenta From now on I consider only two flavor quark matter**Inhomogeneousgap parameter**LOFF phase Pairs with non-zero total momenum**Cristallography**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**Interesting cristallographic structures**P=8Face centered cube(F.C.C.) P=6Body centered cube(B.C.C.)**Gap equation**= Free energy 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 energyof the various structures. How can I compute such a free energy ?**One wave**BCC FCC LOFF Comparison of the free energies BCS (Ruggieri et al. - 2004)**Mantel+hadron superfluid**LOFF, gCFL CFL(if densities arehigh enough) LOFF and compact stars ? If quark matter is present in the core of a neutron star, then the LOFF phase could be realized there.**Fermions are relevant for the thermodynamical properties.**BCS • Spatial symmetries are spontaneously broken Phonons LOFF If LOFF, how can it contribuite to the thermodynamics ? • Gapless fermion dispersion laws**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.**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.