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Nuclear and compact-star matter:. Two general results: Thermodynamics => limiting T > T critical Scalings => No-Criticality. c @ 1/2. Supernova remnant and neutron star in Puppis A (ROSAT x-ray). c @ 1/3. e -. P. Napolitani, Ph. Chomaz, C. Ducoin,

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  1. Nuclear and compact-star matter: • Two general results: • Thermodynamics => limiting T > Tcritical • Scalings => No-Criticality c @ 1/2 Supernova remnant and neutron star in Puppis A (ROSAT x-ray) c @ 1/3 e- P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. HasnaouiGANIL, Caen, France r0 0.1r0 core crust crust core

  2. Nuclear and compact-star matter: • Two general results: • Thermodynamics => limiting T > Tcritical • Scalings => No-Criticality c @ 1/2 Supernova remnant and neutron star in Puppis A (ROSAT x-ray) c @ 1/3 e- P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. HasnaouiGANIL, Caen, France r0 0.1r0 core crust crust core

  3. Nuclear and compact-star matter: Three main differences: • Order N => First order up Tcritical n*=> Continuous • Temperature N => reduces limiting T n*=> increases limiting T • Scalings N => Critical line n*=> No criticality c @ 1/2 Supernova remnant and neutron star in Puppis A (ROSAT x-ray) c @ 1/3 e- P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. HasnaouiGANIL, Caen, France r0 0.1r0 core crust crust core

  4. Collisions Ions Heavy Gas Liquid Dense matter EOS Plasma of Quarks and Gluons 20 200 MeV • Thermodynamics • Mechanical, thermal, chemical properties • Role of Coulomb (Frustration) • Structure of matter • Neutrino transport Critical points (second order) Temperature Temperature Nucleus Density 0 1 5?

  5. Order of Phase transition (infinite systems) 1

  6. Thermodynamical potentials non analytical at Thermodynamical potentials L.E. Reichl, Texas Press (1980) Thermodynamical potential Order of transition: discontinuity in Log Z Ehrenfest’s definition Temperature ß First order: discontinuous EOS: Caloric curve E2 Energy E1 R. Balian, Springer (1982) Temperature ß Order of Phase transition (infinite systems)

  7. Order of Phase transition (infinite systems) Nuclear Matter Case

  8. Any 2-fluids EOS: (e.g. Mean-Field SLy4) • Grand potential • 2 fluids(protons and neutrons) • Coexistence Fold Liquid Gas mp mn Liquid jump • Discontinuity in r • First order transi. • Liquid-gas rp Gas mn mp

  9. Isospin in coexistence Neutron density rn mn mp Proton density rp mp mn

  10. Isospin in coexistence: distillation Neutron density (Except symmetric matter) • Z/A order parameter rn mn mp <= Proton density rp mp mn

  11. Isospin in coexistence: distillation (Except symmetric matter) • Z/A order parameter

  12. Isospin in coexistence: distillation (Except symmetric matter) • Z/A order parameter Liquid: + symmetric Gas: + asymmetric • Isospin distillation

  13. Z/A=cst transformation (Except symmetric matter) • Z/A order parameter • => Z/A=cst transfo. follows the coexistence

  14. Z/A=cst transformation • Z/A order parameter • Continuous P(r) & mq(r) Z/A=cst transformation but • Discontinuous EOS first order transition This is not a plateau • => Z/A=cst transfo. follows the coexistence

  15. Z/A=cst transformation • Z/A order parameter • Continuous P(r) & mq(r) Z/A=cst transformation but • Discontinuous EOS first order transition This is not a plateau • => Z/A=cst transfo. follows the coexistence

  16. Order of Phase transition (infinite systems) Star Matter Case

  17. Electrons & Coulomb c = 0 • Coulomb Divergence => strict neutrality • Single free density => Single chem. pot. • No thermo defined for c≠0 => c not defined = (e + p)/2 = e + p • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞ Star Matter Case

  18. Proton density Electron density rp mp mn Star Matter Case • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞

  19. Star Matter Case function of = e + p strict neutrality • Continuous transformation as function of = e + p • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞

  20. Electron density strict neutrality Star Matter Case function of = e + p • Continuous transformation as function of = e + p • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞

  21. density strict neutrality Star Matter Case function of = e + p • Continuous transformation as function of = e + p • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞

  22. strict neutrality density Star Matter Case = e + p (MeV) function of = e + p • Continuous transformation as function of = e + p • Ex: Mean field free E => Diverge if c≠0 => Is the sum if c= 0 ∞

  23. Coulomb interaction on L-G transition 2

  24. Coulomb expected to reduce L-G transition

  25. Coulomb expected to reduce L-G transition • Nuclei • Reduces instability & bimodality • Reduces limiting temperature Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278

  26. q r  = 2/k Coulomb expected to reduce L-G transition • Supernovae core & neutron* • Reduces pasta phases • Reduces instabilities • Nuclei • Reduces instability & bimodality • Reduces limiting temperature Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278 C. Ducoin, Ph. Ch., F. Gulminelli to be published

  27. q r  = 2/k Coulomb expected to reduce L-G transition • Supernovae core & neutron* • Reduces pasta phases • Reduces instabilities • Nuclei • Reduces instability & bimodality • Reduces limiting temperature Providência, Brito, Avancini, Menezes, Ph. Ch, Phys. Rev. C 73, 025805 (2006) and to appear in PRC Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278

  28. q r  = 2/k Coulomb expected to reduce L-G transition • Supernovae core & neutron* • Reduces pasta phases • Reduces instabilities • Problems: • Phase transition • With critical phenomena • With long range forces • With finite size fluctuations • Approximations not valid • Mean-field not correct Providência, Brito, Avancini, Menezes, Ph. Ch, Phys. Rev. C 73, 025805 (2006) and to appear in PRC

  29. Coulomb expected to reduce L-G transition • Solution: • Phase transition = universal phenomena • Study exactly solvable models eg Ising • Ising (Lattice-Gas) extensively used to study liquid-gas phase transition in nuclei • Problems: • Phase transition • With critical phenomena • With long range forces • With finite size fluctuations • Approximations not valid • Mean-field not correct

  30. Beyond mean-field: Ising*

  31. Beyond mean-field: Ising*

  32. Event distribution: bimodality => phases

  33. Event distribution: bimodality => phases

  34. Phase diagram:

  35. Phase diagram: Ising L=10 Phase diagram Liquid Gas

  36. Phase diagram: Ising L=10 Phase diagram Critical point Ising star • Comparison of Ising model and the Ising* (star matter) Finite size scaling Liquid Gas

  37. Phase diagram: Ising Ising star • Comparison of Ising model with Ising* (star matter) Ising L=10

  38. Ising star Ising Phase diagram: Ising / Ising* • Comparison of Ising model with Ising* (star matter) • Strong increase of the Limiting temperature • not decrease like in MF & nuclei -

  39. Ising star Ising Phase diagram: Ising / Ising* • Comparison of Ising model with Ising* (star matter) • Strong increase of the Limiting temperature • not decrease like in MF & nuclei -

  40. Event distribution:

  41. Event distribution: Ising • Fluctuating partitions at critical point qiqj/rij= ij/rij=>∞ diverging observable • Bimodality below critical point => phase transition Coulomb qiqj/rij Temperature Tc Ising critical point coexistence Nuclear ’ninj

  42. Event distribution: Ising Ising • Fluctuating partitions at critical point qiqj/rij= ij/rij=>∞ diverging observable • Bimodality below critical point => phase transition Coulomb qiqj/rij Temperature Tc Ising Nuclear ’ninj

  43. Event distribution: Ising Ising • Fluctuating partitions at critical point qiqj/rij= ij/rij=>∞ diverging observable Coulomb qiqj/rij Temperature Tc Ising Nuclear ’ninj

  44. Event distribution: Ising / Ising* Ising Ising Star • Fluctuating partitions at critical point • quenched by Coulomb interaction with electrons Coulomb qiqj/rij Tlimit Temperature Tc Ising P~eqiqj/rij Nuclear ninj

  45. Event distribution: Ising / Ising* Ising Ising Star • Fluctuating partitions at critical point • quenched by Coulomb interaction with electrons • The system is driven back to coexistence ie bimodality Coulomb qiqj/rij Tlimit Temperature Tc Ising P~ecqiqj/rij Nuclear ninj

  46. Event distribution: Ising / Ising* Ising Ising Star • Fluctuating partitions at critical point • quenched by Coulomb interaction with electrons Coulomb qiqj/rij Tlimit Temperature Tc Ising Nuclear ninj

  47. Event distribution: Ising / Ising* Ising Ising Star • Fluctuating partitions at critical point • quenched by Coulomb interaction with electrons • Need higher T to suppress bimodality ie higher limiting temperature Coulomb qiqj/rij Tlimit Temperature Tc Ising Nuclear ninj

  48. Event distribution and finite-size scaling

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