Transcript Diapositiva 1 - Istituto Nazionale di Fisica Nucleare

LOFF, the inhomogeneous “faces”
of color superconductivity
Marco Ruggieri
Università degli Studi di Bari
Conversano,
QCD@work2005,
16 – 20 Giugno 2005
High density QCD

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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
Fermi
Surface
BCS:
Pairing with zero total momentum
3
BCS color superconductivity 2
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Phases characterized by diquark
condensation:
Superconductive
Normal
4
In nature………

Fermi momenta of the quarks can
be different, because:

Weak equilibrium

Non-zero masses of the quarks
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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.)
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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
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Comparison of the free
energies
One wave
BCC
FCC
BCS
LOFF
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(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. gCFL
CFL
(if densities are
high enough)
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If LOFF, how can it contribuite
to the thermodynamics ?

Gapless fermion dispersion laws
Fermions are relevant for the
BCSthermodynamical properties.
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Spatial symmetries are
LOFF
spontaneously
broken
Phonons
13
Conlusions and open
questions
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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.
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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.
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