1. 1 Charge Density Fluctuations in the presence of spinodal instabilities Quark-Gluon Plasma - symmetric phase color superconductor Universal properties of the QCD phase diagram: charge fluctuations probe of chiral symmetry restoration and deconfinemnet Fluctuations and spinodal phase separation K. Redlich TCP 1st order Crossover CEP for 2 nd order HG phase -sym. broken A-A collisions

2. 2 PNJL model and chiral phase transition Polyakov loops quantifies repulsive interaction between quarks Generic structure of the phase diagram as expected in QCD and in different chiral models see eg.: M. Asakawa & K. Yazaki; J. Berges & K. Rajagopal, H. Fujii & Ohtani; M. Harada & A. Shibata, M. Halasz et al.; M. Alford et al, A. Hatta & T. Ikeda, Ratti, W. Weise; C. Sasaki, B Schaefer, J. Wambach,.. Large no CEP at finite T

3. 3 Susceptibilities of conserved charges Net quark-number,isovector and electric charge fluctuations No mixing of isospin density with the sigma field due to isospin conservation Hatta & Stephanov TCP 1st order 2nd order B. Friman, C. Sasaki & K.R.

4. 4 Scaling properties: The strength of the singularity at TCP depends on direction in plane along 1st order line any direction not parallel along 2nd order line Going beyond the mean field: B.-J. Schaefer & J. Wambach Z(2) univer. class C.Sasaki, B. Friman & K.R. : Ising See also Y. Hatta, T. Ikeda

5. 5 Scaling properties: The strength of the singularity at TCP depends on direction in plane along 1st order line any direction not parallel along 2nd order line Going beyond the mean field: B.-J. Schaefer & J. Wambach Z(2) univer. class C.Sasaki, B. Friman & K.R. : Ising See also Y. Hatta, T. Ikeda O(4) univer. class

6. 6 Quark and isovector fluctuations along critical line sensitive probes of CEPNon-singular behavior at CEP of To find CEP surch for a non-monotonic behavior of the net quark number susceptibility as a function of or in heavy ion collisions as a function of

7. 7 Ratio of as a probe of deconfinement HRG factorization of pressure: consequently: in HRG In QGP, Ratio of cumulants excellent probe of deconfinement S. Ejiri, F. Karsch, K.R. Bulk properties due to flavor content gap of medium constituents: S. Jeon, V. Koch; M. Asakawa, U. Heinz, B. Muller

8. 8 The nature of the 1 st order chiral phase transition instability of a system: : stable : unstable : spinodal A-B: supercooling (symmetric phase) B-C: non-equilibrium state C-D: superheating (broken phase)

9. 9 Phase diagram in the Nambu-Jona-Lasinio model C.Sasaki, B. Friman & K.R.

10. 10

11. 11 Net-quark fluctuations on spinodals at any spinodal points: Singularity at CEP are the remnant of that along the spinodals CEP spinodals with

12. 12 Experimental Evidence for 1 st order transition Specific heat for constant pressure: Low energy nuclear collisions

13. 13 LGT phase boundary and chemical freezeout At present, the critical curve and CEP obtained in LGT coincide with the chemical freeze-out However: recent LGT results show that: there is no unique value of at ( Y.Aoki at.al) Critical temperature at can be as large as ( M. Cheng et al.)

14. 14 Summary The net-quark number fluctuations through quartic/quadratic cumulants ratio are an excellent probe of deconfinement in HIC at the LHC A non-monotonic change of the net- quark susceptibility in HIC with the collision energy probes the existence of CEP However if spinodal phase separation occurs then: Divergence of charge fluctuations appear across the 1 st order transition along the spinodal lines Non-equilibrium chiral phase diagram:

15. 15 Energy dependent fluctuations & CEP Smooth change of fluctuations with collision energy: no sign of CEP NA49

16. 16 Compressibility of the QGP Large density fluctuations at saturated by fluctuations in HRG Isothermal compressibility: should be large near CEP For the HRG gives: Bulk properties due to flavor content gap of medium constituents: S. Jeon, V. Koch; M. Asakawa, U. Heinz, B. Muller

17. 17 Pressure: 1st order Quark fluctuations and O(4) universality class R. Pisarski, F. Wilczek expected