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Fluctuations of fragment observables

This review covers fluctuations of fragment observables, constraints, susceptibilities, and experimental findings in the context of an ideal gas of fragments. Open questions explore quantitative estimation of fluctuations and dynamics of expansion. The status of the art in theoretical and experimental research is evaluated.

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Fluctuations of fragment observables

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  1. Fluctuations of fragment observables • Introduction: motivation • finite size effects • Theory: fluctuations and constraints • fluctuations and susceptibilities • Experiment: M2, g2, NVZ, sk • Open questions: quantitative estimation of fluctuations • an ideal gas of fragments ? • the dynamics of the expansion A review of the theoretical and experimental status of the art M.D’Agostino - F.Gulminelli

  2. Introduction

  3. Introduction I Historical motivation Diverging fluctuations at a critical point Multifragmentation: opening of phase space large fluctuations of fragment partitions Nautilus 93 Aladin 96 Isis 01

  4. Introduction II Caveat: finite size effects 3D percolation • (1) Smoothing of the phase transition • (2) Conservation constraints and sorting effects X.Campi 88 3D percolation 3D percolation random partitions J.Elliott 00

  5. Introduction III (3) Thermodynamic ambiguities : independence of the density of the fluctuation behavior J.Pan 98 J.Carmona 98 P.Chomaz 00

  6. Need to compare with models and/or quantify the fluctuation peak

  7. Theory

  8. Theory I Fluctuations and constraints c.e. V.V.Begun 05 grancanonical canonical microcanonical Ntot=N++N- N+ Mass conservation versus fluctuations of Amax J.Carmona 03 F.Gulminelli 03 Fluctuations are suppressed if a constraint is applied to a correlated variable

  9. Theory II Fluctuations and constraints F.Gulminelli 01 Volume constraint versus energy/Amax fluctuations J.Carmona 03 Fluctuations are suppressed if a constraint is applied to a correlated variable

  10. Theory III Relation between fluctuations and susceptibilities P.Chomaz 01 Conservation constraint Statistical independence Gaussian approximation from fluct. exact where and sref variance of A1 in the ensemble where only <A> is constrained Ex:

  11. Data

  12. Aladin 96 AGS–BNL 94 20 40 60 Zbound Experiment I Effect of the sorting variable Aladin 96 AGS-BNL 03 Au+Au 400,600 800,1000 A.MeV Au+emulsions Au+Au 35 AMeV Multics 00 Au+C 1AGeV EOS 00

  13. g2 Ar+Al,Ti,Ni Nimrod 04 Ar+Al,Ti,Ni Nimrod 04 EOS 03 NVZ=sNV=s2Zm/<Zm> RMS= sZm/<Z0> Experiment II Size effects Au+C RMS~.15 La+C Au+Au Multics 00 Kr+C RMS~0.03 <E*/A>(MeV) Multics H clusters s/sc E(max) ~ 5 A.MeV m/mc

  14. Experiment III « Configurational energy » fluctuations Multics 04 average kinetic energies lcp-fragment correlations + hypothesis on mass

  15. Experiment IV « Configurational energy » fluctuations Indra Ni+Au 50AMeV Indra Xe+Sn 32AMeV Multics-Miniball Au+Au 35AMeV Au+C 35AMeV Au+Cu 25,35AMeV Indra+Aladin Multics 04 Pre-equilibrium? Radial flow? Neck emission? Au+Au 80AMeV

  16. Experiment V « Configurational energy » fluctuations Multics 04 Nimrod 04 Size effect? Sorting? Side feeding?

  17. Experiment VI « Configurational energy » fluctuations Multics 00 As +- 10% no restriction Au+C 1AGeV Au+Au 35A.MeV Kr+C 1AGeV Source size conservation? Flow effects? Are we looking at the same observable? E*/A E*/A EOS 02

  18. Open questions

  19. Open questions I From theory to data: an ideal gas of fragments ? ? Campi Krivine 04 Lennard Jones CMD thermo QLD aV(l),aS(l) Gulminelli Chomaz 04 Lattice Gas EI QLD

  20. t=0 confined asymptotic Open questions II Out of equilibrium effects: the dynamics of the expansion How far is a freeze out from thermal equilibrium? E=-1.7e E=0.1e E=0.8e Chernomoretz 04 time t=0 confined asymptotic Balenzuela 02

  21. Conclusions • The theoretical connections between fluctuations and susceptibilities are well established but conditions have to be checked • conservation constraint • statistical independence • gaussian distribution • Experimental multiplicities/sizes fluctuations agree reasonably well (in comparable size ranges) • The methodology to extract configurational energy fluctuations is under debate • cluster definition in dense quantum media (Fermi motion?) • the dynamics of the expansion + entrance channel • systematic errors in fluctuations measurements • The challenge is finite systems thermodynamics: it is worthwhile to go on • We need – full comparisons with a well defined protocol and consistency checks - better measurements to assess the effect of the experimental constraints

  22. Open questions VI Out of equilibrium effects: uniformity of phase space Gulminelli Chomaz 02 A.Majka 03 M.Ploszacjack 02 Tsallis entropy

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