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Connection between

Connection between. THE LARGEST LYAPUNOV EXPONENT,DENSITIY FLUCTUATION AND MULTIFRAGMENTATION. in EXCITED NUCLEAR SYSTEMS. Yingxun Zhang (CIAE). Xizhen Wu (CIAE), Zhuxia Li (CIAE). CCAST, Beijing, 2005.8.20. Outline. 1. Motivations. 2. Model. 3. Results & Discussion. 4. Summary.

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Connection between

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  1. Connection between THE LARGEST LYAPUNOV EXPONENT,DENSITIY FLUCTUATION AND MULTIFRAGMENTATION inEXCITED NUCLEAR SYSTEMS Yingxun Zhang (CIAE) Xizhen Wu (CIAE), Zhuxia Li (CIAE) CCAST, Beijing, 2005.8.20

  2. Outline 1. Motivations 2. Model 3. Results & Discussion 4. Summary

  3. MOTIVATIONS Phase transition in finite nuclear system Multifragmentation ? ? ? Anomalous increase of density fluctuation A rapid increase of chaoticity the main goal of this work is to explore the relation between them

  4. (the density fluctuation) (Macroscopic thermodynamical) (the largest lyapunov exponent ) Phase space distance between two trajectories at time nt Measurement of chaoticity In general case: a given trajectory in phase space come back close to the initial state of system Average along an infinite trajectory

  5. Nuclear fragmentation Excited state Nucleons & Clusters A given trajectory in the phase space never come back close to the initial state Average on ensemble at local time finite size effects on critical temperature From calcium to superheavy nuclei

  6. MODEL 1. QMD model The dynamic evolution of an excited nuclei Physics picture The latter stage of the heavy ion collisions 2. Create an initially excited nucleus a). RMF The nuclei in ground states b). Density distribution Each nucleon position & momnetum c). Resampled the momentum T initial temperature

  7. RESULTS & DISCUSSION The relation between the chaoticity and density fluctuation a. LLE In our case Distance in phase space between two events At initial state: avp is average momentum rms is root mean square radius as a function of time Over an ensemble Whose condition is consistent with a hot nucleus at a given temperature

  8. PRC69, 044609(2004) fragmentation take place Dt~45fm/c 208Pb evolution with time l(t) value at the plateau as the LLE

  9. LLE as a function of temperature “Critical temperature” The descent branch The raising branch Due to increase of fluctuation with temperature System breaks up very soon and collective expansion

  10. b. DENSITY FLUCTUATION In QMD model Many-body correlation At T=11MeV Saturation values Abnormal growth and jumps character time for abnormal growth~150fm/c Time evolution of density fluctuation

  11. there is enough time to develop chaotic dynamics during the process of fragment formation The character time for abnormal density fluctuation growth ~150fm/c > The inverse LLE ~ 40 fm/c the abnormal density fluctuation deterministic chaos Small uncertainty in the initial condition Produce a large dynamical fluctuation in final observances.

  12. Saturation values of density fluctuation as a function of temperature

  13. What relation between the LLE &density fluctuation ???? The heterogeneity of the phase density J.P.Eckmann, Rev.Mod.Phys. 57,617(1985), Y.Gu,Phys.Lett.A 149,95(1990) Momentum distribution fluctuation Density fluctuation Cross term ~LLE

  14. The relation between the LLE and the density fluctuation The LLE increase with the density fluctuation increasing. for finite nuclear system

  15. c. MASS DISTRIBUTION OF MULTIFRAGMENTATION Nucleons,and heavy residues Distributed over a wild range Nucleons, and light fragments

  16. For 208Pb, T=11MeV Fisher’s model of liquid-gas phase transition a drop with size A in the vapor At “critical temperature”, Power-law Recently obtained experiment value PRL88(2002) 022701

  17. finite size effect on critical temperature “critical temperature” as a function of the size of systems PRC69, 044609(2004) From Ca to superheavy nuclei Tc increase with the system size

  18. SUMMARY 1. At critical temperature, there appears a plateau in the time evolution of LLE and the density fluctuation show an abnormal growth 2. The time scale of the density fluctuation is much longer than the inverse largest Lyapunov exponent, which means that the chaotic motion can be well developed during the process of fragment formation. 3. The LLE peaks at the same temperature where the density fluctuation grows abnormally and the mass distribution of fragments is fitted well with the Fisher’s power law 4. The critical temperatures increase with system mass, after 197Au it seems to reach a saturation value of about T=11MeV

  19. thanks !

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