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Celebrating Nakamura San's Achievements at Yamagata University

Recollections of impactful collaborations with Nakamura San throughout his esteemed career at Yamagata and Hiroshima University, focusing on lattice group advancements and transport coefficient studies. Congratulations on his 60th birthday!

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Celebrating Nakamura San's Achievements at Yamagata University

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  1. Recollections of collaboration with Nakamura san Nakamura san! Congratulations on your 60th birthday §0His activities and achievements at Yamagata §1First stage of collaboration: Start of new lattice group at Yamagata (-1996) §2Second stage :Yamagata Hiroshima collaboration (-2005) §3Third stage: larger collaboration (2005-) Toward more reliable determination of T.C

  2. §0 Nakamura san’s activity and achievements at Yamagata 1993.4arrive at his post Faculty of Education, Yamagata University 1997.6 move to Hiroshima University the Faculty of Integrated Arts and Sciences Information Media Center He was kind enough to promote the use of the internet for colleagues

  3. 1995 awarded Gordon Bell prize( performance category) using NWT at National Aerospace Laboratory of Japan

  4. He encouraged his students to participate in PSC (parallel software contest ) They had won a prize. Japan-Germany seminar on lattice QCD 1996.3 Yamagata University 1997.8 Bielefeld 1999.10 Kanazawa

  5. §1First step of collaboration: start of new lattice group at Yamagata 1995Transport coefficients from Lattice QCD Thermodynamics Nucl. Phys. B(Proc. Suppl.) 42(1995) N. Masuda, A. Nakamura, S. Sakai, J. Urakawa and F. Shoji 1996 Transport Coefficients of Quark Gluon Plasma for Pure Gauge Models Nucl. Phys. B(Proc. Suppl.) 53(1997) 432-434 A. Nakamura, S. Sakai and K. Amemiya 1997 Transport Coefficients of Quark Gluon Plasma from Lattice Gauge Theory Nucl. Phys.A638(1998) 535c-538c A. Nakamura, S. Sakai and T. Saito Quark Matter ’97 at Tsukuba

  6. Lattice size 163×8 Iwasaki Action at β=3.05, 3.2, 3.3 (1.4<T/Tc<1.8) Before the RHIC resultswas published

  7. §2Second stage (From 1997 to 2005) Yamagata-Hiroshima collaboration §２．１ study of anisotropic lattice Nucl.Phys.B584(2000),pp528 – pp542, S. Sakai, T. Saito and A .Nakamura Physical Review D Vol69, 114504(2004),1-11, S.Sakai and A. Nakamura ηA = ξB/ξR ξＲ=aσ/aτ

  8. 2.2continued the calculation of transport coefficients Lattice size 24^3×8 Iwasaki and standard sction 1.4 < T/Tc < 24 RHICdata was reported It suggested a new states of matter: almost perfect fluid

  9. Our results suggested small η/s ratio. Phy.Rev.Letters Vol94, 072305(2005),1-4 Transport coeffcients of Gluon Plasma from Lattce QCD PoS (LAT2005)(2005),186(Oct) （Lat 20005 Dublin) A. Nakamura and S. Sakai

  10. §3 s of collaboration After RHIC data was reported, some groups start the calculation of T.C H. Mayer Swansea and Seoul?? … We had started larger collaboration (from 2005 ) R. Gupta, Y. Koma, T. Umeda, Y. Nakagawa...

  11. 3.1) Improve the Statistics on 24^3x8 lattice. (Jobs were continued on SX8 at RCNP) the results from 243 ×8 (2010.January) Number of mesurements Improved action: 1.4x107 Standard action: 5.5x107

  12. 3.2) toward the more reliable determination of T.C. difficulty in the study. • To determine the spectral function from Matsubara Green function • Namely Determine continuous function from discrete data MEM seems to be promising. need many data points (data on fine lattice) with small errors To adopt anisotropic lattice may be effective to save CPU time

  13. 3.2.1) a comments on adopting anisotropic lattice ηA = ξB/ξR ist-dependent at short distances t

  14. expected behavior of G12(t) if QGP state is determined by temperature.

  15. 2) how to reduce the fluctuation of G12(t) ①adopt improved action 243x8 lattice

  16. ②Multi-level algorithm (Y. Koma san) ③Energy momentum tensorfrom clover type loops What is needed now Plenty of CPU time on massive computer and Write code which work well on that computer I hope this project will be finished before Nakamura san retires. Finally I would like to express my gratitude to Nakamura san. The study on transport coefficients was hard but exciting, and I have enjoyed the comfortable collaboration with you.

  17. Some mathematician said that life is 20 times 4 First 20 years: time to learn Second 20 years: do job with what he learns Third 20 years: spend some of his time for administration Last 20 years: spend all times for himself

  18. S. Tomonaga said what (Jananease) physicist do when he get old (retire) is grouped into three categories do history do nothing do nonsense

  19. Fluctuation increase at large distances ２４３ｘ８

  20. fluctuation is stronger on anisotropic lattice Improved action at β=4.5 on 243x8 isotropic lattice and 243x16 anisotropic lattice with ζ=2

  21. 3.3MEMによるρの決定 Ｇβ on ＮＴ＞３０ lattice, 統計精度の良いデータ 極めて難しい 方策？ 1) Ｔμνの改善 　　ハドロン（Glue Ball)質量の計算のようにはいかない　 Wall, Box Source ×

  22. 2) 非等方格子の採用 　　格子間隔を温度方向と空間方向で変える 温度aτ 温度 空間　　　　　　　　　　　　　　　　　　　　空間 等方格子：　aσ = aτ　　　　　　　　　非等方格子：　aσ = 2・aτ

  23. 同じaσ､且つ　aσ/aτ=2 にチューニングすれば、 同じt・aτの点では等方格子でも非等方格子でもGβは同じ　　 Nt=4Nt=8 taτ

  24. RIHC results indicate a new state of matter Phenomenology of elliptic flow Perfect fluid：　viscosity~ 0 Jet Quenching mean free path（λ）, mean free time（τ） small Strong coupling system

  25. 輸送係数の摂動計算 A. Hosoya and K. Kajantie, Nucl.Phys.B250(1985),p666 R. Horsley and W. Schoenmaker, Nucl.Phys.B280(1987),p716, and p735. S. Gavin, Nucl.Phys. A435(1987),p826 P.Arnold, G.D.Moore and G. Yaffe,JHEP 0305(2003) 051, (hep-ph/0302165) etc η small αｓlarge

  26. 輸送係数と結合定数との関係 ：(Kinetic Theory) A.Hosoya,M.Sakagami and M.Takao, Annals of Physics 154(1982),229 W.J.Moore, Physical Chemistry, Longmans, London,1958 mean free path： large(g: small) 粘性係数large mean free path small(g: large) 粘性係数 small

  27. 一般に τ:mean free time(mean free path) N：　particle number Kf : kinematical factor τ∝　１/（σρ） σ：　cross section ρ：　density （τ、η）　->small=> strong coupling 系　

  28. ηis also expressed by using the spectral function ρ(ω) of the retarded Green function, 1.3 determination of ρ On a lattice, ρ is determined from Matsubara green functioninstead of calculating retarded Green functions directly, using the fact that the spectral function of them are the same. Where

  29. Difficulty in the determination of is discrete, while ρ(ω) is continuous. Therefore fine resolution in temperature direction (simulation on large NT lattice) is necessary for the accurate determination of it. is quite noisy, that it need much CPU time. We start on a smaller NT lattice, assuming plausible form for ρ(ω) . Simplest non-trivial form is[4], This form is derived by the perturbative calculation of self energy[5]. In this case γ is a decay width.

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