方德清 马余刚 蔡翔舟 田文栋 王宏伟 陈金根 郭威 Shear viscosity to entropy density ratio and liquid-gas phase transition 李绍歆 方德清 马余刚 蔡翔舟 田文栋 王宏伟 陈金根 郭威 2010年07月26日

outline Introduction viscosity and liquid-gas transition our work BUU Model our work viscosity in intermediate energy heavy ion collisions the lowest value of viscosity/entropy? Summary and Conclusions

motivation In ultra relativistic heavy ion collision, we often study the QGP phase and critical phenomenon according to the minimum value of viscosity/entropy. Due to van der Waals nature of the interaction force of nucleon-nucleon, Liquid-gas transition happen in intermediate heavy-ion collisions. the lowest value of viscosity/entropy can be a signal of liquid-gas phase transition phase in nuclear reaction? arXiv:0812.2422

我们的猜测：核液气相变 （红虚线是我们手画的线）： YGM, 云南会议2007 Perfect liquid? 我们的猜测：核液气相变 （红虚线是我们手画的线）： YGM, 云南会议2007 Lacey et al., PRL 98, 092301 (2007)‏

BUU model Description of the model. 1) Mean field 2) Two-body collisions 3) Pauli blocking

Green-kubo formula The Green-Kubo formalism relates linear transport coefficients to near-equilibrium correlations of dissipative fluxes . where if the nucleons are uniformly distributed in space Here t=0 is equilibrium time If volume is fixed PHYSICAL REVIEW C 69, 044901 (2004)‏

temperature Au+Au 50~100MeV r=5fm extract phase space information Boltzmann distribution t=70 fm/c n/n0=1 (n0=0.16) t=100fm/c n/n0=1/2 t=140fm/c n/n0=1/4 Where is the energy of nuclei i 高能段拟合上

Equilibrium Au+Au 50~100MeV Thermodynamic equilibrium( temperature approach to fixed data)‏ Kinetic condition So the equilibrium time t0>=100fm/c Different energy has different t0 pk 趋于定值 t>t0 ,温度变化缓慢

tensor PHYSICAL REVIEW C 69, 044901 (2004)‏ 驰豫时间随入射能量逐渐减小

Entropy density 定体积内熵随入射能量减小 PHYSICAL REVIEW C 69, 044901 (2004)‏

Viscosity / entropy Different incident beam energy(50~100MeV)‏ Temperature (after equilibrium)‏ conclusion: The lowest value of eta/s between 70 and 80MeV. 最低点位置

Conclusion The lowest value of viscosity/entropy between 70 and 80MeV The other way ( power-law and LN(Amax)-S2) show Liquid-gas transition happen when the incident beam energy about 80MeV . problem : the result is sensitivity to the equilibrium time . Improvement: we need more incident energy data other way to calculate state parameter and eta other judgment and experiment data to prove our conclusion

Thanks all !