Phonons and gluons in the crystalline color superconducting phase of QCD

Casalbuoni, R.; Fabiano, E.; Gatto, R.; Mannarelli, Massimo; Nardulli, G.

doi:10.1103/physrevd.66.094006

Cited by 26 publications

(38 citation statements)

References 32 publications

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“…The existence of long-wavelength oscillations with the phonon dispersion law was already noted by Fulde and Ferrell (1964). More recently an effective Lagrangian for phonons in a QCD medium was developed by Casalbuoni et al Casalbuoni, Fabiano, et al, 2002;, and we wish to review it in this section, dedicated predominantly to the QCD LOFF phase. For color superconductivity only the T→0 case is physically interesting and we shall consider only this limit.…”

Section: Phonon and Gluon Effective Lagrangiansmentioning

confidence: 99%

Inhomogeneous superconductivity in condensed matter and QCD

2004

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Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories. CONTENTS

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Section: Phonon and Gluon Effective Lagrangiansmentioning

confidence: 99%

Inhomogeneous superconductivity in condensed matter and QCD

2004

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“…The shear modulus can be related to the coefficients in the low energy effective theory that describes the phonon modes of the crystal [32,51,52]. This effective theory has been analyzed, with its coefficients calculated, for the two-flavor crystalline color superconductor with face-centered cubic symmetry [52]. Extending this analysis to three-flavor crystalline color superconducting phases with the 2Cube45z and CubeX crystal structures is a priority for future work.…”

Section: Conclusion Implications and Future Workmentioning

confidence: 99%

“…In order to immobilize vortices, and hence make glitches a possibility, both the pinning force and the shear modulus must be sufficient. The shear modulus can be related to the coefficients in the low energy effective theory that describes the phonon modes of the crystal [32,51,52]. This effective theory has been analyzed, with its coefficients calculated, for the two-flavor crystalline color superconductor with face-centered cubic symmetry [52].…”

Section: Conclusion Implications and Future Workmentioning

confidence: 99%

Crystallography of three-flavor quark matter

2006

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We analyze and compare candidate crystal structures for the crystalline color superconducting phase that may arise in cold, dense but not asymptotically dense, three-flavor quark matter. We determine the gap parameter ∆ and free energy Ω(∆) for many possible crystal structures within a Ginzburg-Landau approximation, evaluating Ω(∆) to order ∆ 6 . In contrast to the two-flavor case, we find a positive ∆ 6 term and hence an Ω(∆) that is bounded from below for all the structures that we analyze. This means that we are able to evaluate ∆ and Ω as a function of the splitting between Fermi surfaces for all the structures we consider. We find two structures with particularly robust values of ∆ and the condensation energy, within a factor of two of those for the CFL phase which is known to characterize QCD at asymptotically large densities. The robustness of these phases results in their being favored over wide ranges of density. However, it also implies that the Ginzburg-Landau approximation is not quantitatively reliable. We develop qualitative insights into what makes a crystal structure favorable, and use these to winnow the possibilities. The two structures that we find to be most favorable are both built from condensates with face-centered cubic symmetry: in one case, the ud and us condensates are separately face centered cubic; in the other case ud and us combined make up a face centered cube.

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“…The slab can be thought as a local approximation of the CCSC crust, and therefore we expect that the frequency of the crust torsional oscillations has the same qualitative dependence on ν, ρ and the crust thickness, D = R − R c as in Eq. (25).…”

Section: Nonradial Oscillationsmentioning

confidence: 99%

“…The shear modulus of the energetically favored phase can be obtained studying the low energy oscillations of the condensate modulation [23][24][25][26]. In particular, the low energy expansion of the GL Lagrangian of [26] leads to a shear modulus…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic signals from bare strange stars

et al. 2014

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The crystalline color superconducting phase is believed to be the ground state of deconfined quark matter for sufficiently large values of the strange quark mass. This phase has the remarkable property of being more rigid than any known material. It can therefore sustain large shear stresses, supporting torsional oscillations of large amplitude. The torsional oscillations could lead to observable electromagnetic signals if strange stars have a crystalline color superconducting crust. Indeed, considering a simple model of strange star with a bare quark matter surface, it turns out that a positive charge is localized in a narrow shell about ten Fermi thick beneath the star surface. The electrons needed to neutralize the positive charge of quarks spill in the star exterior forming an electromagnetically bounded atmosphere hundreds of Fermi thick. When a torsional oscillation is excited, for example by a stellar glitch, the positive charge oscillates with typical kHz frequencies, for a crust thickness of about one-tenth of the stellar radius, to hundreds of Hz, for a crust thickness of about nine-tenths of the stellar radius. Higher frequencies, of the order of few GHz, can be reached if the star crust is of the order of few centimeters thick. We estimate the emitted power considering emission by an oscillating magnetic dipole, finding that it can be quite large, of the order of 10 45 erg/s for a thin crust. The associated relaxation times are very uncertain, with values ranging between microseconds and minutes, depending on the crust thickness. The radiated photons will be in part absorbed by the electronic atmosphere, but a sizable fraction of them should be emitted by the star.

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Phonons and gluons in the crystalline color superconducting phase of QCD

Cited by 26 publications

References 32 publications

Inhomogeneous superconductivity in condensed matter and QCD

Inhomogeneous superconductivity in condensed matter and QCD

Crystallography of three-flavor quark matter

Electromagnetic signals from bare strange stars

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