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Crossover, fluctuations and Anderson transition in quark matter formation

Crossover, fluctuations and Anderson transition in quark matter formation. Boris Kerbikov,ITEP. The physics of (nuclear matter)  (quark matter) transition. QCD phase diagram. We are here today. T. Triple point (Stephanov). T c. BCS (Son). Hadron gas. CFL. 2SC.  (GeV). 0.3.

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Crossover, fluctuations and Anderson transition in quark matter formation

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  1. Crossover, fluctuations and Anderson transition in quark matter formation Boris Kerbikov,ITEP

  2. The physics of (nuclear matter)  (quark matter) transition QCD phase diagram We are here today T Triple point (Stephanov) Tc BCS (Son) Hadron gas CFL 2SC  (GeV) 0.3 0.6

  3. The interplay of three events • BEC-BCS crossover • Strong fluctuations • Anderson transition (?) Transition region: •  ( 0.3 – 0.5 ) GeV n = - /  (3-5 ) times > n of normal nuclear matter n1/3  1 fm-1

  4. The key parameters describing the NM  QM transition • n1/3  1 – the BCS-BEC crossover parameter, n is the quark number density,  is the qq pair size (for BCS n1/3  103 ) • Gi  10-2 – the Ginzburg-Levanyuk number (Gi  10-12 – 10-14 for BCS ) • kFlmfp  1 fm – Anderson parameter ( l – mean free path ) The three parameters are interconnected

  5. Crossover - what is it? gap Fluctuating pairs Cooper pairs Gas of tightly Bound pairs n1/3 g/g0

  6. 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 Pairing mechanism: 4-fermion interaction ( NJL, or instantons, or gluon echange)  ( 1 – 2 ) fm Quark matter emerges in the crossover regime rather than in BCS

  7. NM  QM transition goes with strong fluctuations Ginzburg – Levanyuk parameter is a measure of fluctuations • Tc ( 40 – 50 ) Mev •  400 Mev In BSC Gi  10-12 – 10-14, in HTSC Gi  10-5 Fluctuations and Crossover Gi  0.4 / ( n1/3  )4 Gi  10- 2 

  8. Color diamagnetism Fluctuations of the gluon field are more important than fluctuations of quark pairs Two effects: • Lowering of the critical temperature T* = Tc ( 1- g22< A2 > ) • First order phase transition instead of second – cubic term in Ginzburg-Landau functional

  9. Anderson localization in quark matter Anderson localization – dynamical diffusion coefficient turns zero due to random impurities Ioffe-Regel criterion kFl  1, l is the quark mean free path Impurities – stochastic field configurations (e.g.,instantons) kF    400 Mev, l  1 fm, close to the mobility edge D =  0 Along with D the gradient term in GL functional is suppressed

  10. 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 interconnected

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