2. Oscillations of the quark-gluon plasma from oscillations to fast thermalization dedicated to Professor Andrzej Białas on the occasion of His 70-th birthday or Wojciech Florkowski

3. 1. Development of the color-flux-tube model by Białas and Czyż development by Białas and Czyż in the series of papers published in the 1980s color-flux-tube model: Casher, Neuberger, Nussinov, PR D20 (1979) 179

4. -A. Białas and W. Czyż, Boost-invariant Boltzmann-Vlasov equations for relativistic quark-antiquark plasma, Phys. Rev. D30 (1984) 2371 -A. Białas and W. Czyż, Chromoelectric flux tubes and the transverse momentum distribution in high-energy nucleus-nucleus collisions, Phys. Rev. D31 (1985) 198 -A. Białas and W. Czyż, Oscillations of relativistic, boost-invariant quark-antiquark plama, Z. Phys. C28 (1985) 255 -A. Białas and W. Czyż, Conversion of color field into q anti-q matter in the central region of high-energy heavy-ion collisions, Nucl. Phys. B267 (1986) 242 -A. Białas and W. Czyż, Production and collective motion of q anti-q plasma in heavy-ion collisions, Acta Phys. Pol. B17 (1986) 635 -and more others...

5. - chromoelectric fields stronger than in „elementary” e + e - annihilations Biro, Nielsen, Knoll, Nucl. Phys. B245 (1984) 449 (increased multiplicity, increased production of strange particles) - oscillations of the quark-antiquark plasma - fast (t 0 <1 fm/c) production of dense matter k number of color charges q which span the initial field, g coupling constant

6. A. Białas, W. Czyż, A. Dyrek, and WF, Oscillations of quark-gluon plasma generated in strong color fields, Nucl. Phys. B296 (1988) 611 time dependence of the chromoelectric field (LHS) and the energy density of quarks and gluons (RHS) for various values of the parameter k

7. time dependence of the average transverse (LHS) and longitudinal (RHS) momentum of quarks and gluons for various values of the parameter k [8 gluon fields are separated into 2 „neutral fields” (chromoelectric field E 3, E 8 ) and 6 „charged gluons” (treated as particles together with quarks)]

8. A. Dyrek and WF, Production of heavy quarks in strong chromoelectric fields, Nuovo Cim. A102 (1989) 1013 the ratio of strange quarks to up and down quarks quantitatively similar results to those obtained by P. Koch, B. Muller, and J. Rafelski, Phys. Rep. 142 (1986) 167

9. 2. Early-thermalization in relativistic heavy-ion collisions A. Białas, Fluctuations of string tension and transverse-mass distribution Phys. Lett. B31 (1999) 301 gaussian fluctuations of the string tension can account for the „thermal” distribution of transverse mass of particles created in decay of a color string 1)the data collected at RHIC suggest that matter is well thermalized and exhibits collective behavior (bound states above T C, Shuryak; plasma instabilities, Mrówczyński; Hawking-Unruh effect, Kharzeev) 2) already in more elementary collisions we observe thermal features, Boltzmann distributions in transverse momentum, Hagedorn, 1960s

10. the measured transverse-momentum spectra have thermal (exponential) shape, Hagedorn, 1960s string models of hadronic collisions use the Schwinger formula Białas: appropriate averaging over κ may produce an exponential function fluctuations may appear due to stochastic nature of the QCD vacuum (H.G. Dosch, Yu. A. Simonov)

11. my personal follow-up of this idea, WF, Schwinger tunneling and thermal character of hadron spectra, Acta Phys. Pol. B35 (2004) 799 quark spectra in the color-flux tube model are exponential due to the dynamic oscillations of the chromoelectric field E

12. oscillations in varying chromoelectric fields may explain the origin of the thermal spectra in heavy-ions but this effect is not capable of describing thermal features observed in elementary processes it is conceivable, however, that the effect of the stochastic vacuum plays an additional role in heavy-ion collisions leading to even more pronounced thermalization effects

13. Instead of Conclusions... Drogi Panie Profesorze! z okazji tego Jubileuszu proszę przyjąć najserdeczniejsze życzenia wielu lat zdrowia i pomyślności, a także podziękowania za wszystkie naukowe inspiracje