1. Scaling properties of multiplicity fluctuations in heavy-ion collisions simulated by AMPT model Yi-Long Xie China University of Geosciences, Wuhan （ Xie Yi-Long, Chen Gang ， et al ， Nucl. Phys. A 920 (2013) 33–44 ）

2. Content Nonlinear Dynamics AMPT model Results of NFM Analysis Discussion of FM’s Scaling Summary China University of Geosciences School of mathematics and physics

3. 1. Nonlinear Dynamics Big local fluctuation implied dynamical factors. China University of Geosciences School of mathematics and physics Bialas ： describe the fluctuation with NFM as follow:

4. 1. Nonlinear Dynamics China University of Geosciences School of mathematics and physics Self-similar FractalSelf-affine Fractal Criterion for existence of fractal

5. 1. Nonlinear Dynamics China University of Geosciences School of mathematics and physics Characterize of Self-similar Fractal: Characterize of Self-affine Fractal Isotropic partition the phase-space Anisotropic partition the phase-space with calculated Hurst exponent Fitting the 1-d NFM with saturation exponents Calculate the Hurst exponent with saturation exponent Wu Y F, Liu L S. Phys Rev Lett, 1993, 70(21):3197-3200

6. collision at region 1. Nonlinear Dynamics Self-similar Fractal China University of Geosciences School of mathematics and physics Self-affine Fractal Hadron collision Agababyan N M, Atayan M R, Charlet M, et al. Phys Lett B, 1996, 382(3):305-311 Abreu P, Adam W, Adye T, et al. Nucl Phys B, 1992, 386(2):471-492

7. The final state system in collisions at region is self-affine fractal 1. Nonlinear Dynamics China University of Geosciences School of mathematics and physics The final state system in hadron collisions is self-affine fractal Does fractal exist in heavy ion collisions? Which kind of fractal? Experiments has shown that: So:

8. A Pictorial View of Micro-Bangs at RHIC: 1. Initial Condition 2. Partonic Cascade 3. Hadronization 4. Hadronic Rescattering 2 AMPT model

9. (a) AMPT v1.11 (Default)(b) AMPT v2.11 (String Melting)

10. 3.1 Results of NFM Analysis China University of Geosciences School of mathematics and physics Tab.1. Fitting parameters for 1-D NFM (q=2). 1. 1-D NFM tends to saturate 2. Saturation exponents: 3. Identical Hurst exponents: Fig.1. 1-D NFM: (q=2).

11. 3.2 Results of NFM Analysis China University of Geosciences School of mathematics and physics Fig.2. The logarithm distribution of 2-D NFM, i.e. Fitting formula ： Show good Scaling Conclusion: Self-Similar Fractal

12. 3.3 Results of NFM Analysis China University of Geosciences School of mathematics and physics 1.Fitting Formula: Same Conclusion: Scaling Feature and Self- similar Fractal Fig.3. The logarithm distribution of 3-D NFM: Tab.2. Fitting parameter for 3-D NFM Tab.3. Effect Fluctuation Strength 2. Fluctuation in heavy ion collision is larger than those in hadron collisions and collisions. Effect Fluctuation Strength: QGP

13. 4. Discussion of FM’s Scaling China University of Geosciences School of mathematics and physics Scaling property is checked again. Fig.4. The distribution of 3-D NFM:Fig.5. Parameter are obtained when fitting the relation ： 1.. 2. Fitting Formula: Not phase transition in AMPT. RudophC. Hwa, M. T. Nazirov, Phys. Rev. Lett. 69 (1992) 1741.

14. 4. Discussion of FM’s Scaling China University of Geosciences School of mathematics and physics Fig.6. The loglog distribution of 2-D NFM in the plane at various intervals 1.Expectation: 2.Indeed, Fluctuation with 3. Due to the limited events, quantitative analysis can’t be made.

15. 4. Discussion of FM’s Scaling China University of Geosciences School of mathematics and physics Fig.7. The distribution of 2-D NFM as a function of, with partition number M=1 rapidly with. Fluctuation in high is actually much larger than that in low. 2D FM on plane(M=1):

16. 5 Summary China University of Geosciences School of mathematics and physics 1. With the data of Au-Au collision events at 200Gev generated by AMPT model, the 1-D NFM is obtained. The obtained Hurst exponent approximately equal to 1 within the error range. 2. Partitioning the phase-space according to Hurst exponent, then calculate the 2-D and 3-D NFMs. They both show good scaling, which means the final state system is self-similar fractal. 3. According to the calculated effect fluctuation strengths, the fluctuation in heavy ion collisions is found to be much smaller than those in hadron-hadron collisions and electron-positron collisions, which may be the signal of QGP. 4. When checking the scaling property again, the parameter can be obtained. Our results is larger than v =1.304 derived in Ginzburg-Landau type of phase transition. AMPT does not include the phase transition. 5. Splitting the pt range into smaller intervals, the in high is expected to be larger than that in low. Due to the limited events, quantitative analysis can’t be made. But if considering the 2D FM on (M=1), we actually see the increasing of fluctuation with the increasing of pt.

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