1. Hua Zheng a and Aldo Bonasera a,b a)Cyclotron Institute, Texas A&M University b)LNS-INFN, Catania-Italy. 12016-3-5 Density and Temperature of Fermions from Quantum Fluctuations

2. Outline  Motivation  Conventional thermometers  New thermometer  Application to CoMD  Summary 2

3. Nuclear Collision 3 Measured in experiment event by event: Mass (A) Charge (Z) Yield Velocity Angular distribution Time correlation The physical quantities in EoS: Pressure (P) Volume (V) or Density ( ) Temperature (T)

4. Conventional thermometers  The slopes of kinetic energy spectra (Tkin)  Discrete state population ratios of selected clusters (Tpop)  Double isotopic yield ratios (Td) 4 A. Bonasera et al., La Rivista del Nuovo Cimento, Vol 23, p1, 2000 S. Albergo et al., IL NUOVO CIMENTO, vol 89 A, N. 1 (1985) M. B. Tsang et al., PRC volume 53, (1996), R1057 J. Pochodzalla et al., CRIS, 96, world scientific, p1 All of them are based on the Maxwell-Boltzmann distribution. No quantum effect has been considered so far.

5. New thermometer 5 A new thermometer is proposed in S. Wuenschel, A. Bonasera et al., Nucl. Phys. A 843 (2010) 1 based on momentum fluctuations A Quadrupole is defined in the direction transverse to the beam axis Its variance is LHS: analyze event by event in experiment RHS: analytic calculation by assuming one distribution When a classical Maxwell-Boltzmann distribution of particles at temperature was assumed

6. Trapped Fermion System 6 Christian Sanner et al., PRL 105, 040402 (2010) Quantum Effect

7. Density and temperature of fermions from quantum fluctuations 7 Density: Multiplicity fluctuations: Wolfgang Bauer, PRC, Volume 51, Number 2 (1995) H. Zheng, A. Bonasera, PLB, 696(2011) 178-181 H. Zheng, A. Bonasera, arXiv: 1112. 4098v1 Quadrupole fluctuations: Fermi Dirac distribution

8. Density and temperature of fermions from quantum fluctuations 8 H. Zheng, A. Bonasera, PLB, 696(2011) 178-181 H. Zheng, A. Bonasera, arXiv: 1112. 4098v1

9. Density and temperature of fermions from quantum fluctuations 9 In the high order case High T These equations can be used in all temperature region

10. Density and temperature of fermions from quantum fluctuations 10 M. Papa et al., PRC, Volume 64, 024612 CoMD: Constrained Molecular Dynamics Model

11. Density and temperature of fermions from quantum fluctuations 11 Circle: proton Square: neutron Triangle: triton Star: He3 H. Zheng, A. Bonasera, arXiv:1105. 0563[nucl-th]B. C. Stein et al, arXiv: 1111.2965v1 Experimental data 32 S+ 112 Sn

12. Proton Neutron Density and temperature of fermions from quantum fluctuations 12 H. Zheng, A. Bonasera, arXiv: 1112. 4098v1R. Wada et al., arXiv: 1110. 3341 v1 L. Qin et al., PRL 108, 172701 (2012)

13. Density and temperature of fermions from quantum fluctuations 13 H. Zheng, A. Bonasera, arXiv: 1112. 4098v1 Up triangle: high order P Open circle: low T approximation P Down triangle: high order N Open square: low T approximation N Up solide triangle: high order P Open triangle: d/p ratio P Down solide triangle: high order N Open star: d/n ratio N

14. Part of Borderie’s talk-IWM2011 14 Tclas-protons FO Tkin Tquant-protons FO

15. Future Plan-Bosons 15 Multiplicity fluctuations: Quadrupole fluctuations: Bose-Einstein distribution

16. Future Plan-Bosons 16 Density: The CoMD code with Boson condensation consideration is in progress, more details see Gianluca Giuliani’s talk

17. Summary Three conventional thermometers are reviewed A new thermometer is introduced The CoMD simulation and experimental results show that we need to consider the quantum effect in NN collision system We derived the high order corrections to density and temperature of fermions 17

18. Thank you! 18

19. Backup 19

20. Density and temperature of fermions from quantum fluctuations 20

21. 21 Density and temperature from quantum fluctuations How to get the multiplicity fluctuations Landau and Lifschitz, Statistical Physics part 1, p342

22. CoMD note 22

23. CoMD 3D picture 23

24. The definition of temperature(1) 24 The 1 st law of thermodynamics is The temperature is The entropy is Thus we get one equation

25. The definition of temperature(2) 25 1) Canonical ensemble 2) Grand canonical ensemble

26. 26 The variance of trapped fermi gas Christian Sanner et al., PRL 105, 040402 (2010)

27. Collecting dots-critical phenomena 27 Panos Christakoglou, arXiv: 1111.4506v1

28. Density and temperature of fermions from quantum fluctuations 28 B. C. Stein et al, arXiv: 1111.2965v1 Experimental evidence of FFQ

29. The constraint in CoMD 29 M. Papa et al., Journal of computational physics 208 (2005) 403-415 Pauli principle

30. Comparison between QMD and CoMD 30 M. Papa et al., PRC, 64, 024612

31. Comparison between Exp data and CoMD 31 Ca+Ca 35MeV/A Large increase of alpha production: Experiment: K. Hagel, et, al, PRC 50, 2017M. Papa et al., PRC, 64, 024612

32. Density and temperature of fermions from quantum fluctuations 32

33. Equation of State 33 The equation which relates the pressure, volume and temperature is called the equation of state (EoS) for a given body. L. D. Landau and E. M. Lifshitz, Statistical Physics, Third Edition, Elsevier Pte Ltd 2007. Example, the EoS for the ideal gas

34. New thermometer 34 S. Wuenschel, et al., Nucl. Phys. A 843 (2010) 1 When a classical Maxwell-Boltzmann distribution of particles at temperature was assumed