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The European Physical Journal C

, Volume 51, Issue 3, pp 677–687 | Cite as

Causal viscous hydrodynamics for central heavy-ion collisions

  • R. Baier
  • P. RomatschkeEmail author
Regular Article - Theoretical Physics

Abstract

We study causal viscous hydrodynamics in the context of central relativistic heavy-ion collisions and provide details of a straightforward numerical algorithm to solve the hydrodynamic equations. It is shown that correlation functions of fluctuations provide stringent test cases for any such numerical algorithm. Passing these tests, we study the effects of viscosity on the temperature profile in central heavy-ion collisions. Also, we find that it is possible to counter-act the effects of viscosity to some extent by re-adjusting the initial conditions. However, viscous corrections are strongest for high-mass particles, signaling the breakdown of hydrodynamic descriptions for large η/s.

Keywords

Hydrodynamic Equation Ideal Hydro Hydrodynamic Description Viscous Hydrodynamic Ideal Hydrodynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. Teaney, J. Lauret, E.V. Shuryak, Phys. Rev. Lett. 86, 4783 (2001)CrossRefADSGoogle Scholar
  2. 2.
    P. Huovinen, P.F. Kolb, U.W. Heinz, P.V. Ruuskanen, S.A. Voloshin, Phys. Lett. B 503, 58 (2001)CrossRefADSGoogle Scholar
  3. 3.
    P.F. Kolb, U.W. Heinz, P. Huovinen, K.J. Eskola, K. Tuominen, Nucl. Phys. A 696, 197 (2001)CrossRefADSGoogle Scholar
  4. 4.
    T. Hirano, K. Tsuda, Phys. Rev. C 66, 054905 (2002)CrossRefADSGoogle Scholar
  5. 5.
    P.F. Kolb, R. Rapp, Phys. Rev. C 67, 044903 (2003)CrossRefADSGoogle Scholar
  6. 6.
    PHENIX Collaboration, K. Adcox et al., Nucl. Phys. A 757, 184 (2005)CrossRefADSGoogle Scholar
  7. 7.
    PHOBOS Collaboration, B.B. Back et al., Nucl. Phys. A 757, 28 (2005)CrossRefADSGoogle Scholar
  8. 8.
    BRAHMS Collaboration, I. Arsene et al., Nucl. Phys. A 757, 1 (2005)CrossRefADSGoogle Scholar
  9. 9.
    STAR Collaboration, J. Adams et al., Nucl. Phys. A 757, 102 (2005)CrossRefADSGoogle Scholar
  10. 10.
    P. Arnold, G.D. Moore, L.G. Yaffe, JHEP 0011, 001 (2000)CrossRefADSGoogle Scholar
  11. 11.
    P. Arnold, G.D. Moore, L.G. Yaffe, JHEP 0305, 051 (2003)CrossRefADSGoogle Scholar
  12. 12.
    P. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005)CrossRefADSGoogle Scholar
  13. 13.
    R.A. Janik, Phys. Rev. Lett. 98, 022302 (2007)CrossRefADSGoogle Scholar
  14. 14.
    E.V. Shuryak, Nucl. Phys. A 750, 64 (2005)CrossRefADSGoogle Scholar
  15. 15.
    T.D. Lee, Nucl. Phys. A 750, 1 (2005)CrossRefADSGoogle Scholar
  16. 16.
    M. Gyulassy, L. McLerran, Nucl. Phys. A 750, 30 (2005)CrossRefADSGoogle Scholar
  17. 17.
    U.W. Heinz, arXiv:nucl-th/0512051Google Scholar
  18. 18.
    U.W. Heinz, Nucl. Phys. A 721, 30 (2003)CrossRefGoogle Scholar
  19. 19.
    B. Muller, J.L. Nagle, arXiv:nucl-th/0602029Google Scholar
  20. 20.
    S.K. Blau, Phys. Today 58N5, 23 (2005)CrossRefGoogle Scholar
  21. 21.
    M. Riordan, W.A. Zajc, Sci. Am. 294N5, 24 (2006)Google Scholar
  22. 22.
    I.R. Klebanov, arXiv:hep-th/0009139Google Scholar
  23. 23.
    F. Karsch, H.W. Wyld, Phys. Rev. D 35, 2518 (1987)CrossRefADSGoogle Scholar
  24. 24.
    A. Nakamura, S. Sakai, Phys. Rev. Lett. 94, 072305 (2005)CrossRefADSGoogle Scholar
  25. 25.
    S. Mrowczynski, Acta Phys. Pol. B 37, 427 (2006)ADSGoogle Scholar
  26. 26.
    P. Arnold, G.D. Moore, Phys. Rev. D 73, 025006 (2006)CrossRefADSGoogle Scholar
  27. 27.
    P. Arnold, G.D. Moore, Phys. Rev. D 73, 025013 (2006)CrossRefADSGoogle Scholar
  28. 28.
    M. Asakawa, S.A. Bass, B. Muller, Phys. Rev. Lett. 96, 252301 (2006)CrossRefADSGoogle Scholar
  29. 29.
    M. Asakawa, S.A. Bass, B. Muller, Prog. Theor. Phys. 116, 725 (2007)CrossRefADSGoogle Scholar
  30. 30.
    E. Iancu, R. Venugopalan, arXiv:hep-ph/0303204Google Scholar
  31. 31.
    P. Romatschke, R. Venugopalan, Phys. Rev. Lett. 96, 062302 (2006)CrossRefADSGoogle Scholar
  32. 32.
    P. Romatschke, A. Rebhan, Phys. Rev. Lett. 97, 252301 (2006)CrossRefADSGoogle Scholar
  33. 33.
    D. Teaney, Phys. Rev. C 68, 034913 (2003)CrossRefADSGoogle Scholar
  34. 34.
    W.A. Hiscock, L. Lindblom, Phys. Rev. D 31, 725 (1985)CrossRefADSGoogle Scholar
  35. 35.
    W. Israel, Ann. Phys. 100, 310 (1976)CrossRefADSGoogle Scholar
  36. 36.
    W. Israel, J.M. Stewart, Phys. Lett. A 58, 213 (1976)CrossRefADSGoogle Scholar
  37. 37.
    W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979)CrossRefADSGoogle Scholar
  38. 38.
    M. Prakash, M. Prakash, R. Venugopalan, G. Welke, Phys. Rep. 227, 321 (1993)CrossRefADSGoogle Scholar
  39. 39.
    A. Muronga, Phys. Rev. Lett. 88, 062302 (2002)CrossRefADSGoogle Scholar
  40. 40.
    A. Muronga, Phys. Rev. Lett. 89, 159901 (2002)CrossRefADSGoogle Scholar
  41. 41.
    A. Muronga, Phys. Rev. C 69, 034903 (2004)CrossRefADSGoogle Scholar
  42. 42.
    A. Muronga, D.H. Rischke, arXiv:nucl-th/0407114Google Scholar
  43. 43.
    A.K. Chaudhuri, U.W. Heinz, J. Phys.: Conf. Ser. 50, 251 (2006)CrossRefGoogle Scholar
  44. 44.
    U.W. Heinz, H. Song, A.K. Chaudhuri, Phys. Rev. C 73, 034904 (2006)CrossRefADSGoogle Scholar
  45. 45.
    R. Baier, P. Romatschke, U.A. Wiedemann, Phys. Rev. C 73, 064903 (2006)CrossRefADSGoogle Scholar
  46. 46.
    R. Baier, P. Romatschke, U.A. Wiedemann, Nucl. Phys. A 782, 313 (2007)CrossRefADSGoogle Scholar
  47. 47.
    K. Tsumura, T. Kunihiro, K. Ohnishi, arXiv:hep-ph/0609056Google Scholar
  48. 48.
    T. Koide, G.S. Denicol, Ph. Mota, T. Kodama, arXiv:hep-ph/0609117Google Scholar
  49. 49.
    P.J.E. Peebles, J.T. Yu, Astrophys. J. 162, 815 (1970)CrossRefADSGoogle Scholar
  50. 50.
    D.N. Spergel et al., arXiv:astro-ph/0603449Google Scholar
  51. 51.
    V. Mukhanov, Physical foundations of cosmology (Cambridge University Press, Cambridge, 2005)zbMATHGoogle Scholar
  52. 52.
    G. Baym, B.L. Friman, J.P. Blaizot, M. Soyeur, W. Czyz, Nucl. Phys. A 407, 541 (1983)CrossRefADSGoogle Scholar
  53. 53.
    Y. Lallouet, D. Davesne, C. Pujol, Phys. Rev. C 67, 057901 (2003)CrossRefADSGoogle Scholar
  54. 54.
    J. Casalderrey-Solana, E.V. Shuryak, D. Teaney, J. Phys.: Conf. Ser. 27, 22 (2005)CrossRefADSGoogle Scholar
  55. 55.
    J. Casalderrey-Solana, E.V. Shuryak, D. Teaney, Nucl. Phys. A 774, 577 (2006)CrossRefADSGoogle Scholar
  56. 56.
    L.P. Kadanoff, P.C. Martin, Ann. Phys. (New York) 24, 419 (1963)zbMATHCrossRefADSGoogle Scholar
  57. 57.
    S. Gavin, M. Abdel-Aziz, Phys. Rev. Lett. 97, 162302 (2006)CrossRefADSGoogle Scholar
  58. 58.
    L.D. McLerran, R. Venugopalan, Phys. Rev. D 49, 2233 (1994)CrossRefADSGoogle Scholar
  59. 59.
    L.D. McLerran, R. Venugopalan, Phys. Rev. D 49, 3352 (1994)CrossRefADSGoogle Scholar
  60. 60.
    A. Krasnitz, R. Venugopalan, Phys. Rev. Lett. 84, 4309 (2000)CrossRefADSGoogle Scholar
  61. 61.
    T. Lappi, Phys. Rev. C 67, 054903 (2003)CrossRefADSGoogle Scholar
  62. 62.
    F. Gelis, R. Venugopalan, Nucl. Phys. A 776, 135 (2006)CrossRefADSGoogle Scholar
  63. 63.
    F. Gelis, R. Venugopalan, Nucl. Phys. A 779, 177 (2006)CrossRefADSGoogle Scholar
  64. 64.
    P. Romatschke, R. Venugopalan, Phys. Rev. D 74, 045011 (2006)CrossRefADSGoogle Scholar
  65. 65.
    K. Fukushima, F. Gelis, L. McLerran, arXiv:hep-ph/0610416Google Scholar
  66. 66.
    D.A. Teaney, J. Phys. G 30, S1247 (2004)CrossRefADSGoogle Scholar
  67. 67.
    A.K. Chaudhuri, Phys. Rev. C 74, 044904 (2006)CrossRefADSGoogle Scholar
  68. 68.
    F. Cooper, G. Frye, Phys. Rev. D 10, 186 (1974)CrossRefADSGoogle Scholar
  69. 69.
    H. von Gersdorff, L.D. McLerran, M. Kataja, P.V. Ruuskanen, Phys. Rev. D 34, 794 (1986)CrossRefADSGoogle Scholar
  70. 70.
    L.D. McLerran, M. Kataja, P.V. Ruuskanen, H. von Gersdorff, Phys. Rev. D 34, 2755 (1986)CrossRefADSGoogle Scholar
  71. 71.
    PHENIX Collaboration, S.S. Adler et al., Phys. Rev. C 69, 034909 (2004)CrossRefADSGoogle Scholar
  72. 72.
    E. Schnedermann, J. Sollfrank, U.W. Heinz, Phys. Rev. C 48, 2462 (1993)CrossRefADSGoogle Scholar
  73. 73.
    P. Romatschke, arXiv:nucl-th/0701032Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Institute for Nuclear TheoryUniversity of WashingtonSeattleUSA

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