Charge neutrality global

Abstract The ground state of dense up and down quark matter under local and global charge neutrality conditions with / -equilibrium has at least four possibilities normal, regular 2SC, gapless 2SC phases, and mixed phase composed of 2SC phase and normal components. The discussion is focused on the unusual properties of gapless 2SC phase at zero as well as at finite temperature. 

The charge neutrality condition can be satisfied locally [6-11] or globally [12, 13]. In the following, we will firstly discuss the homogeneous phase when the charge neutrality is satisfied locally, then discuss the mixed phase when the charge neutrality condition is satisfied globally. 

After the volume fractions have been determined from the condition of the global charge neutrality, we could also calculate the energy density of the corresponding mixed phase,... 

Dense u, d quark matter under local and global charge neutrality conditions in /5-equilibrium has been discussed. 

Under global charge neutrality condition, assuming that the effect of Coulomb forces and the surface tension is small, one can construct a mixed phase composed of positive charged 2SC phase and negative charged normal quark matter. 

The next term on the right side of Ekj. (F.36) is constant in k and involves the product kD k, which does not immediately vanish if averaged over orientations. Nevertheless, we can safely neglect this term. The reason is that it is independent of the position of particle i, with the immediate consequence that the corresponding energy contribution vanishes dtie to the global charge neutrality of the system [see text below Eq. (F.26)]. 

Inspecting the right side of Eq. (F.104) we see that the first term in parentheses is constant. This term is irrelevant because of global charge neutrally 0)- We therefore obtain from Eqs. (F.lOO) and (F.104) as a final expression for the potential from the set of Gaussians... 

Since n(r) > 0, Q(r) decreases monotonically from Q(r0) = A to Q(R) = 0. The latter follows from Eq. 15ii and is in agreement with the requirement of global charge neutrality. It is instructive to use the quantity... 

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