Quark matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons. If one can use the standard model of particle physics, then there is the strongest force (and / or the strong interatstion), which is described by the theory of quantum chromodynamics (QCD). At ordinary temperatures this force just confines the quarks into composite particles-hadrons (corresponding to the QCD energy scale ^ QCD ~ /> 200 MeV) and its effects are not noticeable at longer distances.
The temperature reaches the QCD energy scale (T of order 10 ^ 12 kelvins) to the point where the average inter-quark separation is less than 1 fm and / or the density rises (quark chemical potential mu ~ 400 MeV), the hadrons are melted into their constituent quarks, and the strong interaction becomes the dominant feature of the physics. Such phases are called quark matter or QCD matter. What are the properties of this phase of matter? The phase diagram of quark matter is not well known, either experimentally or theoretically. A commonly conjectured form of the phase diagram. It is applicable to matter in a compact star (such as, for example, neutron stars, and one can assume that inside black holes) where the only relevant thermodynamic potentials are quark chemical potential mu and temperature T. Well, this diagram also shows the typical values of mu and T in heavy-ion collisions and in the early universe. For readers who are not familiar with the concept of a chemical potential, it is helpful to think of μ as a measure of the imbalance between quarks and antiquarks in the system. Higher mu means a stronger bias favoring quarks over antiquarks. At low temperatures there are no antiquarks, and then higher mu generally means a higher density of quarks.Ordinary atomic matter as we know it is really a mixed phase, droplets of nuclear matter (nuclei) surrounded by vacuum, which exists at the low-temperature phase boundary between vacuum and nuclear matter, at mu above 315 MeV and T close to zero. If we increase the quark density (ie increase mu) keeping the temperature low, we move into a phase of more and more compressed nuclear matter. Following this path corresponds to burrowing more and more deeply into a neutron star.The transition from the hadorn.phase to the qgp occurs at temperature 170-240 MeV (or 260MeV???) At low chem.pot., Which is equal to or less than 315 MeV. (There is a small diversion: - Without doubt, strong interactions are described by QCD. And in any case, the matter will be found inside the forerunner of black holes, obeying the laws of QCD (or more accurately, it might be there, or it is likely to be inside the forerunner of black holes). The phase diagram of QCD has two axes: the temperature T and the chemical potential for quark number, mu.
The chemical potential is directly related to the net quark density (ie, the density of quarks-the density of antiquarks): at fixed temperature, larger mu means larger net quark density. Eventually, at an unknown critical value of mu, there is a transition to quark matter. At ultra-high densities we expect to find the color-flavor-locked (CFL) phase of color-superconducting quark matter. In limit of massless quarks, there must be a phase transition related to chiral symmetry breaking. Now let us consider (at least superficially) the situation for the low temperature: Generaly it can be assumed, that the phase transition at T = 0, mu = mu1 extends as a line of phase transition into T-mu-plane, since the argument of asymptotic freedom persists (this phase is not well-known, the properties of such a line (of phase transitions) 're also largely unknown). But the situation at mu = mu0 is much easy. Since, for T> 0, the baryon density n (mu)> 0 even for mu 0 if T = 0 then delta small s = 0. Can be expect that the phase corresponding to our matter (for example a gas) to have a lower particle density than the liquid phase small delta n <0. Since the system absorbs latent heat at the first order phase transition, sigmaQ <0 and delta s <0. Someone can be find that delta T / delta mu <0 with deltan , Is connected to the breaking of an exact sym, the. regions of = 0 and of = / = 0 are separated by one single line transition of phase transitions, ie that the line of the second order phase transitions at high temperatures and the line of first order phase transitions at high densities merge. If the quark masses are not exactly zero, the chir sym never exactly restored and the line of second oder phase transitions to QGP becomes a crossover region. In this case the aforementioned tricritical point does not exit and it is replaced by a bi-critical point. Now one can tell about QCD at finite temperature, for muv = / = 0: Let us now consider the effects induced by increased baryon density, when baryons start overlapping. The most natural prediction relates with asymptotic freedom: as the quarks get nearer and nearer they don't feel the interaction any more, whilst the long range interaction is screened by many body effects. Here that the conclusion is that the system is "nearly free" (ie non confining) hence chir. sym. is realised (one needs some interaction to break the symm. of the action).
And for diverting one can say following, somewhere in the early eighties of the last century, Pisarski and Wilczek showed that if u and d quarks are the only relevant quarks, the phase transition can be second order. Indeed, Monte Carlo simulations indicate that this phase transition is a second-order phase transition in QCD with two-massless quarks. In the real world, the small masses of the u and d quarks smear this transition out into a rapid crossover. The temperature of the crossover is about 170 MeV. One can imagine that now we stay on the other axis at zero temperature, and increase the quark chemical potential. One first jumps from vacuum to nuclear matter-the matter that makes up atomic nuclei. This jump is definitely a first-order phase transition. But,of course, what happens at higher chemical potential, or densities, is less clear. At intermediate densities one can expect some other phases. QCD matter is the prime example of a system in which many such chemical potentials appear.
Color superconductivity is a phenomenon predicted to occur in quark matter if the baryon density is sufficiently high (well above nuclear density) .

Physicists are currently following the following lines of research on color superconductivity:

1.Performing calculations of the phase structure down to medium density using a highly simplified model of QCD, the Nambu-Jona-Lasinio (NJL) model, which is not a controlled approximation, but is expected to yield semi-quantitative insights.

2.Performing calculations in the infinite density limit, to get some idea of the behavior at one edge of the phase diagram.
3.Performing astrophysical calculations, using NJL models or effective theories, to see if there are observable signatures by which one could confirm or rule out the presence of specific color superconducting phases in nature

Well, and yet one can tell about this condition, as «Glasma» ....

Well u can see here//sina.sharif.edu/~sadooghi/Physics%20Colloquium-4.pdf ;-))))