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Crossover, fluctuations and Anderson transition in quark matter formation Boris Kerbikov,ITEP The physics of (nuclear matter) (quark matter) transition QCD phase diagram T Triple point (Stephanov) We are here today Tc BCS (Son) Hadron gas CFL 2SC 0.3 0.6 μ (GeV) The interplay of three events • BEC-BCS crossover • Strong fluctuations • Anderson transition (?) The key parameters describing the NM QM transition • The three parameters are interrelated Crossover - what is it? gap Cooper pairs Fluctuating pairs Gas of tightly Bound pairs g/g0 Crossover for Quarks In 2SC phase u- and d-quarks are paired, s- is out of the game Pairing pattern: scalar, color 3, flavor singlet qi C 3 ij 5q j C 2 4 charge conjugation 3 color symmetry is broken Pairing mechanism: 4-fermion interaction ( NJL, or instantons, or gluon exchange) Quark matter emerges in the crossover regime rather than in BCS NM QM transition goes with strong fluctuations Ginzburg – Levanyuk parameter is a measure of fluctuations 4 Tc 27 Tc Gi 80 28 (3) 4 4 Color diamagnetism Fluctuations of the gluon field are more important than fluctuations of quark pairs Two effects: • Lowering of the critical temperature • First order phase transition instead of second – cubic term in Ginzburg-Landau functional Anderson localization in quark matter Anderson localization – dynamical diffusion coefficient turns zero due to random impurities Ioffe-Regel criterion , l is the quark mean free path Impurities – stochastic field configurations (e.g.,instantons) close to the mobility edge D= 0 Along with D the gradient term in GL functional is suppressed CONCLUSIONS • The dynamics of NM QM transition is ill known • The phenomenology of NM QM transition includes three main events: 1) Crossover from strong coupling/low density to weak coupling/high density (BCS) 2) Strong fluctuations including color diamagnetism 3) Possible Anderson localization of quarks The three events are interrelated