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Holographic thermalization

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Abstract

We consider the transition of a quantum field system toward the state of thermal equilibrium based on the holographic description using the duality between the quantum field system in the d-dimensional Minkowski space and the gravity theory in the (d+1)-dimensional anti-de Sitter space. In this construction, the thermalization in the d-dimensional space is described in the holographic language as the formation of a black hole in the (d+1)-dimensional space. We use a holographic model of thermalization of the quark-gluon plasma describing the black hole formation by the Vaidya metric. We show that evaporation of the black hole, also modeled by the Vaidya metric, leads to an interesting effect in the d-dimensional space: thermalization occurs only at small distances and is impossible in the infrared region. In the considered model, the thermal behavior at small distances is possible only during a certain time, after which the dethermalization process begins.

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References

  1. J. Adams et al. (STAR Collaboration), Nucl. Phys. A, 757, 102–183 (2005); arXiv:nucl-ex/0501009v3 (2005).

    Article  ADS  Google Scholar 

  2. M. Gyulassy and L. McLerran, Nucl. Phys. A, 750, 30–63 (2005); arXiv:nucl-th/0405013v2 (2004).

    Article  ADS  Google Scholar 

  3. E. V. Shuryak, Nucl. Phys. A, 750, 64–83 (2005); arXiv:hep-ph/0405066v1 (2004).

    Article  ADS  Google Scholar 

  4. E. Lancu, “QCD in heavy ions collisions,” arXiv:1205.0579v1 [hep-ph] (2012).

    Google Scholar 

  5. N. N. Bogolyubov, Stud. Stat. Mech., 1, 1–118 (1962).

    Google Scholar 

  6. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics [in Russian], Nauka, Moscow (1971); English transl., Consultants Bureau, New York (1974).

    Google Scholar 

  7. V. V. Kozlov, Gibbs Ensemble and Nonequilibrium Statistical Mechanics [in Russian], RKhD, Moscow (2008).

    Google Scholar 

  8. V. S. Vladimirov, Proc. Steklov Inst. Math., 61, 3–158 (1961).

    Google Scholar 

  9. E. Fermi, Progr. Theoret. Phys., 5, 570–583 (1950).

    Article  MathSciNet  ADS  Google Scholar 

  10. L. D. Landau, Izv. Akad. Nauk SSSR. Ser. Fiz., 17, 51–64 (1953).

    Google Scholar 

  11. F. Gelis, “The early stages of a high energy heavy ion collision,” arXiv:1110.1544v1 [hep-ph] (2011).

    Google Scholar 

  12. B. Müller and A. Schäfer, “Entropy creation in relativistic heavy ion collisions,” arXiv:1110.2378v1 [hep-ph] (2011)

    Google Scholar 

  13. I. V. Volovich, Theor. Math. Phys., 164, 1128–1135 (2010).

    Article  MATH  Google Scholar 

  14. P. M. Chesler and D. Teaney, “Dynamical Hawking radiation and holographic thermalization,” arXiv: 1112.6196v1 [hep-th] (2011).

    Google Scholar 

  15. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, “Gauge/string duality, hot QCD, and heavy ion collisions,” arXiv:1101.0618v2 [hep-th] (2011).

    Google Scholar 

  16. V. Balasubramanian and S. F. Ross, Phys. Rev. D, 61, 044007 (2000); arXiv:hep-th/9906226v1 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  17. I. Ya. Aref’eva, Phys. Part. Nucl., 41, 835–843 (2010); arXiv:0912.5481v1 [hep-th] (2009).

    Article  Google Scholar 

  18. S. S. Gubser, S. S. Pufu, and A. Yarom, Phys. Rev. D, 78, 066014 (2008); arXiv:0805.1551v1 [hep-th] (2008).

    Article  ADS  Google Scholar 

  19. S. S. Gubser, S. S. Pufu, and A. Yarom, JHEP, 0911, 050 (2009); arXiv:0902.4062v1 [hep-th] (2009).

    Article  ADS  Google Scholar 

  20. L. Alvarez-Gaume, C. Gomez, A. Sabio Vera, A. Tavanfar, and M. A. Vazquez-Mozo, JHEP, 0902, 009 (2009); arXiv:0811.3969v1 [hep-th] (2008).

    Article  ADS  Google Scholar 

  21. S. Lin and E. Shuryak, Phys. Rev. D, 79, 124015 (2009); arXiv:0902.1508v2 [hep-th] (2009).

    Article  ADS  Google Scholar 

  22. P. M. Chesler and L. G. Yaffe, Phys. Rev. Lett., 106, 021601 (2011); arXiv:1011.3562v1 [hep-th] (2010).

    Article  ADS  Google Scholar 

  23. I. Y. Aref’eva, A. A. Bagrov, and E. A. Guseva, JHEP, 0912, 009 (2009); arXiv:0905.1087v4 [hep-th] (2009).

    Article  MathSciNet  ADS  Google Scholar 

  24. I. Y. Aref’eva, A. A. Bagrov, and L. V. Joukovskaya, JHEP, 1003, 002 (2010); arXiv:0909.1294v2 [hep-th] (2009).

    Article  ADS  Google Scholar 

  25. I. Y. Aref’eva, A. A. Bagrov, and E. O. Pozdeeva, JHEP, 1205, 117 (2012); arXiv:1201.6542v2 [hep-th] (2012).

    Article  ADS  Google Scholar 

  26. E. Kiritsis and A. Taliotis, “Multiplicities from black-hole formation in heavy-ion collisions,” arXiv:1111.1931v2 [hep-ph] (2011).

    Google Scholar 

  27. P. M. Chesler and L. G. Yaffe, Phys. Rev. Lett., 102, 211601 (2009); arXiv:0812.2053v2 [hep-th] (2008).

    Article  MathSciNet  ADS  Google Scholar 

  28. S. Bhattacharyya and S. Minwalla, JHEP, 0909, 034 (2009); arXiv:0904.0464v2 [hep-th] (2009).

    Article  MathSciNet  ADS  Google Scholar 

  29. U. H. Danielsson, E. Keski-Vakkuri, and M. Kruczenski, Nucl. Phys. B, 563, 279–292 (1999); arXiv:hep-th/9905227v2 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. V. E. Hubeny, M. Rangamani, and T. Takayanagi, JHEP, 0707, 062 (2007); arXiv:0705.0016v3 [hep-th] (2007).

    Article  MathSciNet  ADS  Google Scholar 

  31. J. Abajo-Arrastia, J. Aparicio, and E. López,, JHEP, 1011, 149 (2010); arXiv:1006.4090v1 [hep-th] (2010).

    Article  ADS  Google Scholar 

  32. V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Müller, A. Schäfer, M. Shigemori, and W. Staessens, Phys. Rev. Lett., 106, 191601 (2011) arXiv:1012.4753v3 [hep-th] (2010).

    Article  ADS  Google Scholar 

  33. V. Balasubramanian, A. Bernamonti, J. de Boer, N. Copland, B. Craps, E. Keski-Vakkuri, B. Müller, A. Schäfer, M. Shigemori, and W. Staessens, Phys. Rev. D, 84, 026010 (2011) arXiv:1103.2683v1 [hep-th] (2011).

    Article  ADS  Google Scholar 

  34. R. Callan, J.-Y. He, and M. Headrick, JHEP, 1206, 081 (2012); arXiv:1204.2309v1 [hep-th] (2012).

    Article  ADS  Google Scholar 

  35. I. Ya. Aref’eva and I. V. Volovich, Phys. Lett. B, 433, 49–55 (1998); arXiv:hep-th/9804182v2 (1998).

    Article  MathSciNet  ADS  Google Scholar 

  36. I. V. Volovich, V. A. Zagrebnov, and V. P. Frolov, Theor. Math. Phys., 29, 1012–1021 (1976).

    Article  Google Scholar 

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    I. Ya. Arefeva & I. V. Volovich

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  1. I. Ya. Arefeva
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  2. I. V. Volovich
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Correspondence to I. Ya. Arefeva.

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Dedicated to Vasilii Sergeevich Vladimirov on his 90th birthday

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 3, pp. 216–227, March, 2013.

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Arefeva, I.Y., Volovich, I.V. Holographic thermalization. Theor Math Phys 174, 186–196 (2013). https://doi.org/10.1007/s11232-013-0016-2

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