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QCD 相転移の臨界点近傍における 非平衡ダイナミクスについて

QCD 相転移の臨界点近傍における 非平衡ダイナミクスについて. の１コメント. 北沢正清（京大） , 国広悌二（京大基研 ), 根本幸雄 (RIKEN-BNL). CONTENTS. T. 1, Introduction 2, Collective Mode in CSC 3, Effective Equation for Collective Mode 4, Numerical Simulation 5, Summary and Outlooks. critical endpoint. Chiral symmetry breaking.

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QCD 相転移の臨界点近傍における 非平衡ダイナミクスについて

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  1. QCD相転移の臨界点近傍における非平衡ダイナミクスについてQCD相転移の臨界点近傍における非平衡ダイナミクスについて の１コメント 北沢正清（京大）,国広悌二（京大基研),根本幸雄(RIKEN-BNL) CONTENTS T 1, Introduction 2, Collective Mode in CSC 3, Effective Equation for Collective Mode 4, Numerical Simulation 5, Summary and Outlooks critical endpoint Chiral symmetry breaking Color superconductivity (CSC) m 0

  2. Main New Results given in This Talk derive equation for the collective mode of the pair field above CSC, position of pole: (determine A, B microscopically) in linear response theory. D (x) T x D (x) x m 0 l=2p/k

  3. 1,Introduction Phase Transitions and Fluctuations in QCD At the critical point of the second order phase transitions, fluctuation diverges. W(D) fluctuation of order parameter field chiral transition critical end point (CEP) CSC transition RHIC D SPS might be responsible for various observables. T AGS ? susceptibilities GSI,J-PARC baryon number, chiral, etc… ?? light sigma meson transport coefficient 2SC CFL ??? Stephanov, Rajagopal, Shuryak / Berdnikov, Rajagopal / Hatta, Ikeda / Fukushima / Fujii / Hatta, Stephanov m 0 another CEP?

  4. Fluctuation of pair field in CSC M.K., T.Koide, T.Kunihiro, Y.Nemoto, PRD 65, 091504 (2002) Spectral Function of Pair Field ε→０ （Ｔ→ＴＣ） ＋ ＋・・・ As T is lowered toward TC, The peak of r becomes sharp. The peak survives up toe ~ 0.2 Thouless criterion r(k=0,w =0)diverges at T=TC. electric SC：e ~ 0.005 provided the second order transition,

  5. mDependence of Pseudogap Pseudogap in quark DOS! Depth of the pseudogap hardly changes with m.

  6. 2,Collective Mode in CSC Model Nambu-Jona-Lasinio model (2-flavor,chiral limit)： t：SU(2)F Pauli matrices l：SU(3)C Gell-Mann matrices C :charge conjugation operator Parameters: so as to reproduce Klevansky(1992), T.M.Schwarz et al.(1999) M.K. et al., (2002)

  7. Response Function of Pair Field Linear Response external field: expectation value of induced pair field: Retarded Green function Fourier transformation with Matsubara formalism RPA approx.: where,

  8. Analytic Properties ofQ(k,w)

  9. Im Q(k,w) 1st term: pair creation 3,4th term: scattering Collective mode w~0 k~0 near Tc 2nd term: cf.) in the chiral phase transition H.Fujii, PRD67 (2003) 094018

  10. Cutoff Scheme Since ImQ is free from UV divergence, we calculate it without cutoff. Then, we obtain a simple form, Re Q is calculated from the dispersion relation, (with 3-momentum cutoff) Notice: which ensures

  11. Collective Mode in CSC M.K., T.Koide, T.Kunihiro, Y.Nemoto, PRD 65, 091504 (2002) Spectral Function of Pair Field ε→０ （Ｔ→ＴＣ） ＋ ＋・・・ As T is lowered toward TC, The peak of r becomes sharp. The peak survives up toe ~ 0.2 Thouless criterion r(k=0,w =0)diverges at T=TC. electric SC：e ~ 0.005 provided the second order transition,

  12. k z Pole of Collective Mode Collective Mode pair field Dind(k,w(k)) can be created with an infinitesimal Dex pole of the response function Notice: pole locates in the lower half plane k z first sheet second sheet

  13. Numerical Results m=400MeV k=0 ,50,100,… e =0 ,0.2 ,… ,0.8 for k=0 k=0MeV k=200MeV e=0 e=0.2 e=0.4 k=100MeV k=300MeV Our calculation shows, Poles locate in one direction in the complex plane. It is not pure imaginary. linear quadratic damped oscillation

  14. 3,Effective Equation for Collective Mode Near the crtical temperature, X-1=g-1+Q expands, Notice Thouless criterion: The solution of collective mode (X-1=0) reads, here, : real : complex

  15. : real : complex TDGL equation second time derivative term can appear when particle-hole symmetry is broken pure imaginary Notice: pure imaginary in sigma mode of cSB H. Fujii Particle-hole asymmetry in CSC caused the real part of w. It decreases as m increases.

  16. Numerical Check for m=400MeV (Tc=40.04MeV) Im w(k) :Full calculation :Lowest expansion k Lowest expansion reproduces the full calculations well. up to covers the region where valid collective mode appear.

  17. 4,Numerical Simulation Time Evolution of Pair Field As T is lowered toward Tc, e =0.01 lifetime of the collective mode becomes longer. large momentum mode is not affected at all near Tc. e =0.05 Damped oscillation, but heavy damping e =0.1 k =0 MeV k =50 MeV e =0.5 k =100 MeV k =150 MeV k =200 MeV

  18. Fluctuations in Coordinate Space in infinite matter initial condition: 200fm e =0.1 e =0.01 e =0.5 Dt=200fm t Long wave length (low momentum) fluctuations survives. Time scale of CSC is longer than the one of cSB.

  19. Summary We calculated the collective mode of pair field in CSC. We derived effective equation which describes non-equilibrium dynamics of the pair-field near Tc and low momentum, and confirmed that nature of the collective mode is damped oscillation. The collective mode with pole near the origin might affect various observables collective mode: (w,k) cf, in cSB:

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