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During the last years, the investigation of quark matter at finite temperature and density has become one of the QCD focal points. Based on model calculations it has been predicted that at densities 3-5 times larger than the normal nuclear density the system is unstable with respect to the formation of quark-quark Cooper-pair condensate. This phenomenon is called color superconductivity since diquarks belong to 3 color channel. At present there is a fair understanding of color superconductivity physics in the regime of ultra-high density when a, is small. It took quite some time before it has been realized1?’ that halfway between the nuclear matter phase and color superconducting state lies a new state unlike anything seen before. Shortly after the formulation of the BCS theory it has been realized that in one extreme case fermions can pair strongly forming compact nuclear-like states while at the other end of the spectrum they can pair weakly forming Cooper pairs. The continuous transition between the two regimes is called the BEC-BCS crossover (transition from Bose-Einstein condensation to BardeenCooper-Schrieffer regime). The dimensionless crossover parameter in n 1 I 3 ~ , where n is the characteristic length of pair correlation when the system is in the BCS regime and S is the root of the mean square radius of the bound state when the system is in the strong coupling regime. The crossover occurs at n1/3c 1. Calculations within the framework of the NJL-type models show that the gap equation acquires a nontrivial solution A # 0 when the quark chemical potential reaches the value p N 0.4 GeV which corresponds to n1l3 N 1 h-’. The pair size in this region is E N 2 fm, so that N 1 (for electron superconductors n1I3< 2 lo3). We see that N M --f QM transition brings the system to the crossover regime and not to color superconducting state. The transition region is also characterized by strong fluctuations of both quark and gluon fields. The two phenomena crossover and strong fluctuations, are interrelated as we shall see from Eq. (1) below. Due to fluctuating quark pairs the energy spectrum develops a pseudogap instead of the true gap typical for the BCS regime. Fluctuation contribution to the physical quantities and the width of the fluctuation region is measured by the Ginzburg-Levanyuk number Gi which can be estimated as

CROSSOVER, FLUCTUATIONS AND ANDERSON TRANSITION IN QUARK MATTER FORMATION