Condition charge neutrality

Abstract We investigate the phase structure of color superconducting quark matter at intermediate densities for two- and three flavor systems. We thereby focus our attention on the influence of charge neutrality conditions as well as /3-equilibrium on the different phases. These constraints are relevant in the context of quark matter at the interior of compact stars. We analyze the implications of color superconductivity on compact star configurations using different hadronic and quark equations of state. 

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. 

If a macroscopic chunk of quark matter is created in heavy ion collisions or exists inside the compact stars, it must be in color singlet. So in the following discussions, color charge neutrality condition is always satisfied. 

Now, we discuss the role of electrical charge neutrality condition. If a macroscopic chunk of quark matter has nonzero net electrical charge density tiq, the total thermodynamical potential for the system should be given by... 

Figure 2. The graphical representation of the solution to the charge neutrality conditions (thick dash-dotted line) and the solution to the gap equation for three different values of the diquark coupling constant (thick solid and dashed lines). The intersection points represent the solutions to both. The thin solid line divides two qualitatively different regions, A < S/i and A > S/i. The results are plotted for fi = 400 MeV and three values of diquark coupling constant Go = r/Gs with i] = 0.5, i] = 0.75, and i] = 1.0.

We have discussed the homogeneous 2-flavor quark matter when charge neutrality conditions are satisfied locally, and found that the local charge neutrality conditions impose very strong constraints on determining the ground state of the system. 

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. 

In order to fulfill the charge neutrality condition one can construct a homogeneous mixed phase of these states using the Gibbs conditions [33]. 

Figure 6. Solutions of the gap equations and the charge neutrality condition (solid black line) in the /// vs //, plane. Two branches are shown states with diquark condensation on the upper right (A > 0) and normal quark matter states (A = 0) on the lower left. The plateau in between corresponds to a mixed phase. The lines for the /3-equilibium condition are also shown (solid and dashed straight lines) for different values of the (anti-)neutrino chemical potential. Matter under stellar conditions should fulfill both conditions and therefore for //,( = 0 a 2SC-normal quark matter mixed phase is preferable.

The bond energy per atom, when the local charge neutrality condition eqn (7.59) is satisfied, is given by... 

If the chemical reactions described by eqns (1.184), (1.185), and (1.187) are in chemical equilibrium, the following charge neutrality condition in a crystal must hold... 

We shall now develop an exact expression for Dl which includes the coupling of Vcu and Of through the charge neutrality condition given by eqn (1.188). Starting with the first equation in eqn (1.196) and following a similar procedure to that used in developing eqn (1.193), we can get ... 

In the derivation, the hopping conduction of the oxygen vacancies inside the interconnector [33], the conservation of the charge neutrality condition in the mixed conduction of the oxygen vacancies and the holes, and the unity of the electronic transference number are assumed. It has been reported [34] that Dv is experimentally given by... 

Discussion Acetic acid is soluble in water and partially ionized, resulting in four components HAc, Ac-, H+, and H20. However, now there is a reaction, HAc H+ + Ac, which gives an equilibrium relationship, Ka = H+ Ac /aiiAc> as well as the charge neutrality condition. f ind = 2, yielding / = 2 for the solution in equilibrium with its vapor, the same results as for ethanol-water. 

With this (79) and the charge neutrality condition (75) yield... 

As one example of a coupled-currents theory, the growth of very thick oxide films under local space-charge neutrality conditions will be considered in detail in the following section. 

See Shockley (5) for a demonstration of this conclusion. The essential point here is that the holes are in much better equilibrium across the junction because their concentratiou on the n-side is much larger than is the concentration of electrons on the p-side. In consequence the electrochemical potential (quasi-Fermi level) for holes is essentially constant across the junction while the quasi-Fermi level for electrons takes on whatever gradient is required to satisfy the continuity and charge neutrality conditions. 

Oxygen nonstoichiometry of the perovskites Lai rxB03 (B = Cr, Mn, Co, Fe) and its relationship with electrical properties and oxygen diffusion has been studied extensively [159-161]. T) ical nonstoichiometry data for Lai. r FeOs. and for some other perovskites as obtained from gravimetric analysis and cou-lometric titration are given in Fig. 10.11. At small oxygen deficiency, acceptor dopants are the majority defects. The charge neutrality condition then becomes. 

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