Statistical facets of DCC formation

Carsten Greinergif
Institut für Theoretische Physik, Universität Giessen,
D-35392 Giessen, Germany

tex2html_wrap_inline81 Langevin dynamics

- Brownian motion with colored noise: nonmarkovian Langevin dynamics

- Effective semi-classical action for the soft modes in the tex2html_wrap_inline87-theory

- Stochastic interpretation of Kadanoff-Baym equations

In my talk I first gave a brief review of some ideas behind the use of a semi-classical Langevin treatment of the low momentum modes with tex2html_wrap_inline91 in thermal quantum field theory. This was based on a work [1], which concerns a principle strategy within the influence functional technique for obtaining an effective real-time action for the soft modes by integrating out the hard thermal modes. From another perspective I have also discussed how one can give the famous (non-equilibrium) Kadanoff-Baym equations a stochastic interpretation by means of (quantum) Langevin dynamics [2].

tex2html_wrap_inline81 Stochastic DCC formation

- Langevin description of the DCC formation within the linear tex2html_wrap_inline97model

- Dissipation and fluctuation

- Pion number distribution in various scenarios

- Cumulant expansion of the pion number distribution

In the second part I adressed recent work [3, 4], where by applying a microscopically motivated Langevin description of the linear sigma model, we investigated for various different scenarios the stochastic evolution of a disoriented chiral condensate (DCC) in a rapidly expanding system. I stressed the important role of (understanding) dissipation and fluctuations during the evolution of the DCC order parameter. By choosing some idealized global parameters for the expansion, our findings show that an experimentally feasible DCC, if it does exist in nature, has to be a rare event with some finite probability. The statistical distribution tex2html_wrap_inline105 of final emitted pion number out of domains shows a striking nonpoissonian and nontrivial behaviour. Unusual events out of sample contain a multiple in the number of pions compared to the average. One should indeed interpret those particular events as semi-classical `pion bursts' similar to the mystique Centauro candidates. The further analysis of this unusual distribution by means of the cumulant expansion shows that the reduced higher order factorial cumulants tex2html_wrap_inline107 for tex2html_wrap_inline109 exhibit an abnormal, exponentially increasing tendency. We advocate that an analysis by means of the higher order cumulants serves as a new and powerful signature. In conclusion, the occurence of a rapid chiral phase transition (and thus DCCs) might then probably only be identified experimentally by inspecting higher order facorial cumulants tex2html_wrap_inline111 (tex2html_wrap_inline109) for taken distributions of low momentum pions.


C. Greiner and B. Müller, Phys. Rev. D 55, 1026 (1997).

C. Greiner and S. Leupold, Ann. Phys. 270, 328 (1998).

T.S. Biró and C. Greiner, Phys. Rev. Lett. 79, 3138 (1997).

Z. Xu and C. Greiner, `Stochastic treatment of Disoriented Chiral Condensates within a Langevin description', hep-ph/9910562.


Laurence Yaffe
Tue Nov 23 18:46:15 PST 1999