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Equilibration in φ4 theory in 3+1 dimensions

Alejandro Arrizabalaga1,2, Jan Smit1, and Anders Tranberg1,3

  • 1Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
  • 2National Institute for Nuclear and High-Energy Physics (NIKHEF), Kruislaan 409, 1098 SJ, Amsterdam, The Netherlands
  • 3Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, East Sussex BN1 9QH. United Kingdom

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Phys. Rev. D 72, 025014 – Published 28 July, 2005

DOI: https://doi.org/10.1103/PhysRevD.72.025014

Abstract

The process of equilibration in φ4 theory is investigated for a homogeneous system in 3+1 dimensions and a variety of out-of-equilibrium initial conditions, both in the symmetric and broken phase, by means of the 2PI effective action. Two Φ-derivable approximations including scattering effects are used: the two-loop and the basketball, the latter corresponding to the truncation of the 2PI effective action at O(λ2). The approach to equilibrium, as well as the kinetic and chemical equilibration is investigated.

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References (82)

  1. U. W. Heinz and P. F. Kolb, Nucl. Phys. A702, 269 (2002).
  2. R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001).
  3. D. Molnar and M. Gyulassy, Nucl. Phys. A697, 495 (2002).
  4. J. Berges, S. Borsányi, and C. Wetterich, Phys. Rev. Lett. 93, 142002 (2004).
  5. P. Romatschke and M. Strickland, Phys. Rev. D 68, 036004 (2003).
  6. P. Arnold and J. Lenaghan, Phys. Rev. D 70, 114007 (2004).
  7. P. Arnold, J. Lenaghan, G. D. Moore, and L. G. Yaffe, Phys. Rev. Lett. 94, 072302 (2005).
  8. A. Rebhan, P. Romatschke, and M. Strickland, Phys. Rev. Lett. 94, 102303 (2005).
  9. J. S. Schwinger, Proc. Natl. Acad. Sci. U.S.A. 37, 452 (1951).
  10. P. M. Bakshi and Mahanthappa, J. Math. Phys. (N.Y.) 4, 1 (1963).
  11. P. M. Bakshi and T. K. Mahanthappa, J. Math. Phys. (N.Y.) 4, 12 (1963).
  12. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964).
  13. L. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).
  14. P. Danielewicz, Ann. Phys. (N.Y.) 152, 239 (1984).
  15. K.-c. Chou, Z.-b. Su, B.-l. Hao, and L. Yu, Phys. Rep. 118, 1 (1985).
  16. E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988).
  17. S. Mrówczyński and P. Danielewicz, Nucl. Phys. B342, 345 (1990).
  18. C. Greiner and S. Leupold, Ann. Phys. (N.Y.) 270, 328 (1998).
  19. J.-P. Blaizot and E. Iancu, Phys. Rep. 359, 355 (2002).
  20. F. Cooper, J. Dawson, S. Habib, and R. D. Ryne, quant-ph/9610013, 1996.
  21. T. Altherr and D. Seibert, Phys. Lett. B 333, 149 (1994).
  22. G. Aarts, G. F. Bonini, and C. Wetterich, Phys. Rev. D 63, 025012 (2001).
  23. M. Sallé, J. Smit, and J. C. Vink, Phys. Rev. D 64, 025016 (2001).
  24. M. Sallé and J. Smit, Phys. Rev. D 67, 116006 (2003).
  25. D. Boyanovsky, H. J. de Vega, R. Holman, and J. F. J. Salgado, Phys. Rev. D 54, 7570 (1996).
  26. S. Y. Khlebnikov and I. I. Tkachev, Phys. Rev. Lett. 79, 1607 (1997).
  27. L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. D 56, 3258 (1997).
  28. J. García-Bellido and A. D. Linde, Phys. Rev. D 57, 6075 (1998).
  29. D. Boyanovsky et al., Phys. Rev. D 51, 4419 (1995).
  30. G. N. Felder et al., Phys. Rev. Lett. 87, 011601 (2001).
  31. G. N. Felder, L. Kofman, and A. D. Linde, Phys. Rev. D 64, 123517 (2001).
  32. J.-I. Skullerud, J. Smit, and A. Tranberg, J. High Energy Phys. 08 (2003) 045.
  33. A. Arrizabalaga, J. Smit, and A. Tranberg, J. High Energy Phys. 10 (2004) 017.
  34. A. Krasnitz and R. Venugopalan, Nucl. Phys. B557, 237 (1999).
  35. A. Krasnitz and R. Venugopalan, Phys. Rev. Lett. 84, 4309 (2000).
  36. A. Krasnitz, Y. Nara, and R. Venugopalan, Phys. Rev. Lett. 87, 192302 (2001).
  37. T. Lappi, Phys. Rev. C 67, 054903 (2003).
  38. A. H. Mueller, Nucl. Phys. B558, 285 (1999).
  39. G. Aarts and J. Smit, Nucl. Phys. B511, 451 (1998).
  40. G. Aarts and J. Smit, Phys. Rev. D 61, 025002 (2000).
  41. G. Aarts, G. F. Bonini, and C. Wetterich, Nucl. Phys. B587, 403 (2000).
  42. D. Boyanovsky, C. Destri, and H. J. de Vega, Phys. Rev. D 69, 045003 (2004).
  43. G. Aarts and J. Berges, Phys. Rev. Lett. 88, 041603 (2002).
  44. K. Blagoev, F. Cooper, J. Dawson, and B. Mihaila, Phys. Rev. D 64, 125003 (2001).
  45. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
  46. J. Berges and J. Cox, Phys. Lett. B 517, 369 (2001).
  47. G. Baym and L. P. Kadanoff, Phys. Rev. 124, 287 (1961).
  48. Y. B. Ivanov, J. Knoll, and D. N. Voskresensky, Nucl. Phys. A657, 413 (1999).
  49. D. J. Bedingham, Phys. Rev. D 69, 105013 (2004).
  50. G. Aarts and J. Berges, Phys. Rev. D 64, 105010 (2001).
  51. S. Juchem, W. Cassing, and C. Greiner, Phys. Rev. D 69, 025006 (2004).
  52. F. Cooper, J. F. Dawson, and B. Mihaila, Phys. Rev. D 67, 051901 (2003).
  53. F. Cooper, J. F. Dawson, and B. Mihaila, Phys. Rev. D 67, 056003 (2003).
  54. J. Berges, Nucl. Phys. A699, 847 (2002).
  55. G. Aarts et al., Phys. Rev. D 66, 045008 (2002).
  56. B. Mihaila, Phys. Rev. D 68, 036002 (2003).
  57. J. Berges and J. Serreau, Phys. Rev. Lett. 91, 111601 (2003).
  58. J. Berges, S. Borsányi, and J. Serreau, Nucl. Phys. B660, 51 (2003).
  59. A. Arrizabalaga and J. Smit, Phys. Rev. D 66, 065014 (2002).
  60. M. E. Carrington, G. Kunstatter, and H. Zaraket, Eur. Phys. J. C 42, 253 (2005).
  61. E. A. Calzetta, Int. J. Theor. Phys. 43, 767 (2004).
  62. J. O. Andersen and M. Strickland, Phys. Rev. D 71, 025011 (2005).
  63. J. S. Schwinger, J. Math. Phys. (N.Y.) 2, 407 (1961).
  64. H. van Hees and J. Knoll, Phys. Rev. D 65, 025010 (2002).
  65. H. Van Hees and J. Knoll, Phys. Rev. D 65, 105005 (2002).
  66. J.-P. Blaizot, E. Iancu, and U. Reinosa, Nucl. Phys. A736, 149 (2004).
  67. J. Berges, S. Borsanyi, U. Reinosa, and J. Serreau, Phys. Rev. D 71, 105004 (2005).
  68. F. Cooper, B. Mihaila, and J. F. Dawson, Phys. Rev. D 70, 105008 (2004).
  69. U. Reinosa, in Strong and Electroweak Matter 2002: Proceedings of the SEWM2002 Meeting, edited by Michael G. Schmidt (World Scientific, Singapore, 2003).
  70. A. Arrizabalaga, Ph.D. thesis, University of Amsterdam, 2004.
  71. M. Sallé, J. Smit, and J. C. Vink, Nucl. Phys. B625, 495 (2002).
  72. M. Sallé, Phys. Rev. D 69, 025005 (2004).
  73. D. Boyanovsky, I. D. Lawrie, and D. S. Lee, Phys. Rev. D 54, 4013 (1996).
  74. D. Boyanovsky et al., Phys. Rev. D 52, 6805 (1995).
  75. E.-k. Wang and U. W. Heinz, Phys. Rev. D 53, 899 (1996).
  76. P. Arnold and O. Espinosa, Phys. Rev. D 47, 3546 (1993).
  77. S. Jeon, Phys. Rev. D 47, 4586 (1993).
  78. M. Sallé, J. Smit, and J. C. Vink, in Proceedings of SEWM 2002: Strong and Electroweak Matter (Ref. [69]).
  79. G. Baym, Phys. Rev. 127, 1391 (1962).
  80. M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, 1996).
  81. S. Jeon, Phys. Rev. D 52, 3591 (1995).
  82. D. Boyanovsky, M. D’Attanasio, H. J. de Vega, and R. Holman, Phys. Rev. D 54, 1748 (1996).

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Phys. Rev. D 72, 025014– Published 28 July, 2005
  • Received 25 May 2005

© 2005 American Physical Society

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