HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 121 (2009) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 121 No. 3 (2009) pp. 555-575

[ Full Text PDF : NO CHARGE (428K) ]

Towards a Theory of Entropy Production in the Little and Big Bang

Teiji Kunihiro,1 Berndt Müller,2,3 Akira Ohnishi2 and Andreas Schäfer2,4

1Department of Physics, Kyoto University, Kyoto 606-8502, Japan
2Yukawa Institute for Theoretical Physics, Kyoto University,
Kyoto 606-8502, Japan
3Department of Physics, Duke University, Durham, NC 27708, USA
4Institut für Theoretische Physik, Universität Regensburg,
D-93040 Regensburg, Germany

(Received October 6, 2008)

Abstract:

We propose a broadly applicable formalism for the description of coarse grained entropy production in quantum mechanical processes. Our formalism is based on the Husimi transform of the quantum state, which encodes the notion that information about any quantum state is limited by the experimental resolution. We show in two analytically tractable cases (the decay of an unstable vacuum state and reheating after cosmic inflation) that the growth rate of the Wehrl entropy associated with the Husimi function approaches the classical Kolmogorov-Sinaï entropy. We also discuss various possible applications of our formalism, including the production of entropy in the early stages of a relativistic heavy ion collision.

Subject Index : 056, 228, 231, 435
URL : http://ptp.ipap.jp/link?PTP/121/555/
DOI : 10.1143/PTP.121.555

[ Full Text PDF : NO CHARGE (428K) ]  Citation:

References:

  1. S. Nakajima, Prog. Theor. Phys. 20 (1958), 948[IPAP].
  2. R. Zwanzig, J. Chem. Phys. 33 (1960), 1338[AIP Scitation]; Phys. Rev. 124 (1961), 983[APS].
  3. H. Mori, Prog. Theor. Phys. 33 (1965), 423[IPAP].
  4. B. Robertson, Phys. Rev. 144 (1966), 151[APS].
  5. A. O. Caldeira and A. J. Leggett, Physica A 121 (1983), 587[CrossRef].
  6. R. Balian, Y. Alhassid and H. Reinhardt, Phys. Rep. 131 (1986), 1[CrossRef].
  7. J. Rau and B. Müller, Phys. Rep. 272 (1996), 1[CrossRef].
  8. V. Latora and M. Baranger, Phys. Rev. Lett. 82 (1999), 520[APS].
  9. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, 1991).
    H.-J. Stockmann: Quantum Chaos: An Introduction (Cambridge University Press, 2007).
    F. Haake, Quantum Signatures of Chaos (Springer, 2008).
  10. M. Srednicki, J. of Phys. A 29 (1996), L75[IoP STACKS].
  11. K. Husimi, Proc. Phys.-Math. Soc. Jpn. 22 (1940), 246.
  12. W. H. Zurek and J. P. Paz, Phys. Rev. Lett. 72 (1994), 2508[APS].
  13. A. K. Pattanayak and P. Brumer, Phys. Rev. E 56 (1997), 5174[APS].
    A. Gammal and A. K. Pattanyak, Phys. Rev. E 75 (2007), 036221[APS].
  14. D. Monteoliva and J. P. Paz, Phys. Rev. Lett. 85 (2000), 3373[APS]; Phys. Rev. E 64 (2001), 056238[APS].
  15. A. Wehrl, Rev. Mod. Phys. 50 (1978), 221[APS].
  16. A. Sugita, J. of Phys. A 36 (2001), 9081[IoP STACKS].
  17. A. Sugita, Phys. Rev. E 65 (2002), 036205[APS].
  18. M. Toda and K. Ikeda, Phys. Lett. A 124 (1987), 165[CrossRef].
  19. P. B. Greene, L. Kofman, A. D. Linde and A. A. Starobinsky, Phys. Rev. D 56 (1997), 6175[APS].
  20. B. A. Bassett, S. Tsujikawa and D. Wands, Rev. Mod. Phys. 78 (2006), 537[APS].
  21. R. Jackiw, J. Math. Phys. 9 (1968), 339[AIP Scitation].
  22. M. Hillery, R. F. O'Connell, M. O. Scully and E. P. Wigner, Phys. Rep. 106 (1984), 121[CrossRef].
  23. A. Ohnishi and J. Randrup, Ann. of Phys. 253 (1997), 279[CrossRef].
  24. I. Bengtsson and K. Zyczkowski, Geometry of Quantum States (Cambridge, 2006).
  25. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).
  26. T. Kita, J. Phys. Soc. Jpn. 75 (2006), 114005[IPAP].
  27. Yu. B. Ivanov, J. Knoll and D. N. Voskresensky, Nucl. Phys. A 672 (2000), 313[CrossRef].
  28. A. Nishiyama, arXiv:0810.5003[e-print arXiv].
  29. H. T. Elze and U. W. Heinz, Phys. Rep. 183 (1989), 81[CrossRef].
  30. F. Gelis, S. Jeon and R. Venugopalan, arXiv:0706.3775[e-print arXiv].
  31. I. Arsene et al., Nucl. Phys. A 757 (2005), 1[CrossRef].
    B. Back et al., Nucl. Phys. A 757 (2005), 28[CrossRef].
    J. Adams et al., Nucl. Phys. A 757 (2005), 102[CrossRef].
    K. Adcox et al., Nucl. Phys. A 757 (2005), 184[CrossRef].
  32. S. Pal and S. Pratt, Phys. Lett. B 578 (2004), 310[CrossRef].
  33. B. Müller and K. Rajagopal, Eur. Phys. J. C 43 (2005), 15.
  34. U. W. Heinz and P. F. Kolb, Nucl. Phys. A 702 (2002), 269[CrossRef].
  35. B. Müller and A. Schäfer, Phys. Rev. C 73 (2006), 054905[APS].
  36. R. J. Fries, B. Müller and A. Schäfer, arXiv:0807.1093[e-print arXiv].
  37. K. Geiger and B. Müller, Nucl. Phys. B 369 (1992), 600[CrossRef].
  38. G. R. Shin and B. Müller, J. of Phys. G 29 (2003), 2485[IoP STACKS].
  39. Z. Xu and C. Greiner, Phys. Rev. C 71 (2005), 064901[APS].
  40. A. Krasnitz, Y. Nara and R. Venugopalan, Nucl. Phys. A 717 (2003), 268[CrossRef].
  41. A. Krasnitz, Y. Nara and R. Venugopalan, Nucl. Phys. A 727 (2003), 427[CrossRef].
  42. T. Lappi, Phys. Rev. C 67 (2003), 054903[APS].
  43. H. Fujii and K. Itakura, Nucl. Phys. A 809 (2008), 88[CrossRef].
  44. A. Iwazaki, arXiv:0803.0188[e-print arXiv].
  45. S. Mrowczynski, Acta Phys. Polon. B 37 (2006), 427.
  46. P. Arnold, J. Lenaghan, G. D. Moore and L. G. Yaffe, Phys. Rev. Lett. 94 (2005), 072302[APS].
  47. A. Rebhan, P. Romatschke and M. Strickland, Phys. Rev. Lett. 94 (2005), 102303[APS].
  48. D. Kharzeev and K. Tuchin, J. High Energy Phys. 09 (2008), 093[IoP STACKS].
  49. F. Karsch, D. Kharzeev and K. Tuchin, Phys. Lett. B 663 (2008), 217[CrossRef].
  50. A. Dumitru, E. Molnar and Y. Nara, Phys. Rev. C 76 (2007), 024910[APS].
  51. G. Torrieri and I. Mishustin, Phys. Rev. C 78 (2008), 021901[APS].
  52. R. J. Fries, B. Müller and A. Schäfer, Phys. Rev. C 78 (2008), 034913[APS].
  53. M. Isse, T. Hirano, R. Mizukawa, A. Ohnishi, K. Yoshino and Y. Nara, Int. J. Mod. Phys. E 16 (2007), 2338.
  54. K. Fukushima, F. Gelis and L. McLerran, Nucl. Phys. A 786 (2007), 107[CrossRef].
  55. S. G. Matinyan, E. B. Prokhorenko and G. K. Savvidy, JETP Lett. 44 (1986), 138; Nucl. Phys. B 298 (1988), 414[CrossRef].
  56. B. Müller and A. Trayanov, Phys. Rev. Lett. 68 (1992), 3387[APS].
  57. T. S. Biró, C. Gong, B. Müller and A. Trayanov, Int. J. Mod. Phys. C 5 (1994), 113.
  58. J. Bolte, B. Müller and A. Schäfer, Phys. Rev. D 61 (2000), 054506[APS].
  59. S. Mrowczynski and B. Müller, Phys. Rev. D 50 (1994), 7542[APS].
  60. C. Gong, B. Müller and T. S. Biró, Nucl. Phys. A 568 (1994), 727[CrossRef].
  61. Y. V. Kovchegov, Phys. Rev. D 54 (1996), 5463[APS].

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2010 All rights reserved.