Advertisement

Transport Properties of Quark–Gluon Plasmas

  • Werner EbelingEmail author
  • Vladimir E. Fortov
  • Vladimir Filinov
Chapter
Part of the Springer Series in Plasma Science and Technology book series (SSPST)

Abstract

Hydrodynamic simulations of relativistic heavy-ion collisions require knowledge, not only of the thermodynamic properties of the QGP, but also of the transport properties. While significant progress in calculations of the thermodynamic properties of QGP has been made in recent years, the transport properties are still poorly accessible using lattice QCD (Meyer 2007). It is therefore crucial to devise reliable and manageable theoretical tools for a quantitative description of non-Abelian QGP, both in and out of equilibrium. Unfortunately, the DPIMC method itself cannot directly predict transport properties. To simulate quantum QGP transport and thermodynamic properties in a unified approach, it is reasonable to combine the path integral and Wigner (in phase space) formulations of quantum mechanics. As will be shown below, to calculate kinetic coefficients according to the quantum Kubo formulas, the DPIMC method can be used to generate initial conditions (equilibrium quasiparticle configurations) for virtual dynamical Wigner trajectories in color phase space, describing the time evolution for space, momentum, and color variables. Correlation functions and kinetic coefficients are calculated as averages of Weyl’s symbols for dynamic quantum operators along these trajectories. The basic ideas of this approach have been published in (Filinov 2011). This method is applicable to systems with arbitrarily strong interactions. The self-diffusion coefficient and viscosity of the strongly coupled QGP have been calculated using this approach.

References

  1. D. Banerjee, S. Datta, R. Gavai, P. Majumdar, Phys. Rev. D 85, 14510 (2012)Google Scholar
  2. S.A. Bass, Nucl. Phys. A 862–863, 174 (2011)CrossRefGoogle Scholar
  3. A. Belendez, D.I. Mendez, M.L. Alvarez, C. Pascual, T. Belende, Int. J. Mod. Phys. B 23, 521 (2009)ADSCrossRefGoogle Scholar
  4. S. Cho, I. Zahed, Phys. Rev. C 82, 054907 (2010)ADSCrossRefGoogle Scholar
  5. G. Ciccotti, C. Pierleoni, F. Capuani, V. Filinov, Comp. Phys. Comm. 121–122, 452 (1999)CrossRefGoogle Scholar
  6. H.T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz, W. Soeldner, Phys. Rev. D 86, 14509 (2012)ADSCrossRefGoogle Scholar
  7. J.D. Doll, D.L. Freeman, T.L. Beck, Adv. Chem. Phys. 78, 61–127 (1990)CrossRefGoogle Scholar
  8. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)zbMATHGoogle Scholar
  9. V.S. Filinov, Yu.B Ivanov, V.E. Fortov, M. Bonitz, P.R. Levashov, Phys. Rev. C 87, 35207 (2013)Google Scholar
  10. V.S. Filinov, M. Bonitz, Y.B. Ivanov, V.V. Skokov, P.R. Levashov, V.E. Fortov, Contrib. Plasma. Phys. 51, 322 (2011)ADSCrossRefGoogle Scholar
  11. V.S. Filinov, J. Mol. Phys. 88, 1517–1529 (1996)ADSCrossRefGoogle Scholar
  12. V. Filinov, Y. Medvedev, V. Kamskii, Mol. Phys. 85(4), 711 (1995)ADSCrossRefGoogle Scholar
  13. V. Filinov, P. Thomas, I. Varga, T. Meier, M. Bonitz, V. Fortov, S. Koch, Phys. Rev. B 65, 165124 (2002)ADSCrossRefGoogle Scholar
  14. B.A. Gelman, E.V. Shuryak, I. Zahed, Phys. Rev. C 74, 44908 (2006); ibid. 74, 44909 (2006)Google Scholar
  15. P. Gossiaux, J. Aichelin, T. Gousset, Prog. Theor. Phys. Suppl. 193, 110 (2012); P.B. Gossiaux, J. Aichelin, M. Bluhm, T. Gousset, M. Nahrgang, S. Vogel, K. Werner. Nucl. Phys. A 910–911, 301 (2013)Google Scholar
  16. M. He, R.J. Fries, R. Rapp, Phys. Rev. Lett. 110, 112301 (2013); arXiv:1204.4442 [nucl-th]
  17. A.S. Khvorostukhin, V.D. Toneev, D.N. Voskresensky, Nucl. Phys. A 845, 106 (2010)ADSCrossRefGoogle Scholar
  18. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets (World Scientific Publishing Co., Pte. Ltd., Singapore, 2004)CrossRefzbMATHGoogle Scholar
  19. YuL. Klimontovich, Doklady Akademii Nauk SSSR 108, 1033 (1956)Google Scholar
  20. P. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005)ADSCrossRefGoogle Scholar
  21. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (PhysMathLit, Moscow, 2008)zbMATHGoogle Scholar
  22. A.S. Larkin, V.S. Filinov, Phys. Lett. A 377, 1171 (2013)ADSMathSciNetCrossRefGoogle Scholar
  23. A.S. Larkin, V.S. Filinov, Phys. Lett. A 378, 1876 (2014)ADSMathSciNetCrossRefGoogle Scholar
  24. H.B. Meyer, Phys. Rev. D 76, 101701 (2007)ADSCrossRefGoogle Scholar
  25. T.D. Newton, E.P. Wigner, Rev. Mod. Phys. 21, 3 (1949)CrossRefGoogle Scholar
  26. D.E. Potter, Computational Physics (Wiley, Chichester, 1973)zbMATHGoogle Scholar
  27. Y.B. Rumer, A.I. Fet, Group Theory and Quantum Fields (Nauka, Moscow, 1977)Google Scholar
  28. I.M. Ryzhik, I.S. Gradshteyn, Table of Integrals, Series, and Products (PhysMathLit, Moscow, 1963)zbMATHGoogle Scholar
  29. V. Tatarskii, Sov. Phys. Uspekhi 26, 311 (1983)ADSCrossRefGoogle Scholar
  30. N. Wiener, J. Math. Phys. 2, 132 (1923)CrossRefGoogle Scholar
  31. E. Wigner, Phys. Rev. Phys. Rev. 40, 749 (1932); 46, 1002 (1934)Google Scholar
  32. S.K. Wong, Nuovo Cimento A 65, 689 (1970)ADSCrossRefGoogle Scholar
  33. O.I. Zav’jalov, Proc. Steklov Inst. Math. 228, 126 (2000)Google Scholar
  34. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Plenum Press, New York, 1974)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Werner Ebeling
    • 1
    Email author
  • Vladimir E. Fortov
    • 2
  • Vladimir Filinov
    • 3
  1. 1.Institut für PhysikHumboldt Universität BerlinBerlinGermany
  2. 2.Russian Academy of SciencesMoscowRussia
  3. 3.Joint Institute for High TemperaturesRussian Academy of SciencesMoscowRussia

Personalised recommendations