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

2. High density QCD Color Superconductivity
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. Pairing with zero total momentum
BCS color superconductivity
Superficie di Fermi
Fermi Surface
BCS:
Usare la figura della sfera di fermi per parlare degli impulsi utili per al dinamica.
Pairing with zero total momentum

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

5. 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 ?

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

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

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

10. 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.
How can I compute such a free energy ?
Gap equation =
Free energy

11. Comparison of the free energies
One wave
BCC
FCC
Dire che la procdura di smearing può essere ripetuta per le diverse strutture.
BCS
LOFF
(Ruggieri et al )

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

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

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. 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.