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Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase

R. Casalbuoni·M. Ciminale·M. Mannarelli·G. Nardulli·M. Ruggieri·R. Gatto
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Abstract

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $δμ$, we get that the octahedron is energetically favored from $δμ=Δ_0/\sqrt 2$ to $0.95Δ_0$, where $Δ_0$ is the gap for the homogeneous phase, while in the range $0.95Δ_0-1.32Δ_0$ the face centered cube prevails. At $δμ=1.32Δ_0$ a first order phase transition to the normal phase occurs.

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R. Casalbuoni, M. Ciminale, M. Mannarelli, G. Nardulli, M. Ruggieri, R. Gatto. 2004-04-09. Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase. https://doi.org/10.1103/physrevd.70.054004

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