Skip to main content

Part of the book series: NATO Science Series: B: ((NSSB,volume 368))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. DeTar, Quark-gluon plasma in numerical simulations of QCD, in Quark gluon plasma 2, R, Hwa ed., World Scientific 1995.

    Google Scholar 

  2. A. Ukawa, Nucl. Phys. Proc. Suppl. 53 (1997) 106.

    Article  ADS  Google Scholar 

  3. A. Smilga, Physics of thermal QCD, hep-ph/9612347.

    Google Scholar 

  4. E. Shuryak, Comments Nucl. Part. Phys. 21 (1994) 235.

    Google Scholar 

  5. C. Bernard, T. Blum, C. DeTar, S. Gottlieb, U. Heller, J. Hetrick, K. Rummukainen, R. Sugar, D. Toussaint and M. Wingate, Phys. Rev. Lett. 78 (1997) 598.

    Article  ADS  Google Scholar 

  6. T. Banks and A. Casher, Nucl. Phys. B169 (1980) 103.

    Article  ADS  MathSciNet  Google Scholar 

  7. O. Bohigas, M. Giannoni, Lecture notes in Physics 209 (1984) 1; O. Bohigas, M. Giannoni and C. Schmit, Phys. Rev. Lett. 52 (1984) 1.

    Article  MathSciNet  ADS  Google Scholar 

  8. H. Leutwyler and A. Smilga, Phys. Rev. D46 (1992) 5607.

    ADS  MathSciNet  Google Scholar 

  9. J. Gasser and H. Leutwyler, Phys. Lett. 188B(1987) 477.

    ADS  Google Scholar 

  10. E.V. Shuryak and J.J.M. Verbaarschot, Nucl. Phys. A560 (1993) 306.

    ADS  Google Scholar 

  11. S. Nishigaki, Phys. Lett. 387 B (1996) 707.

    MathSciNet  Google Scholar 

  12. G. Akemann, P. Damgaard, U. Magnea and S. Nishigaki, Nucl. Phys. B 487[FS] (1997) 721.

    Article  ADS  MathSciNet  Google Scholar 

  13. E. Brézin, S. Hikami and A. Zee, Nucl. Phys. B464 (1996) 411.

    Article  ADS  Google Scholar 

  14. T. Guhr and T. Wettig, Universal spectral correlations of the Dirac operator at finite temperature, hep-th/9704055, Nucl. Phys. B (in press); T. Guhr and T. Wettig, J. Math. Phys. 37 (1996) 6395.

    Google Scholar 

  15. A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Nucl. Phys. B479 (1996) 707.

    Article  ADS  Google Scholar 

  16. A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Universality of correlation functions in. random matrix models of QCD, hep-th/9704056, Nucl. Phys. B (in press).

    Google Scholar 

  17. J.J.M. Verbaarschot, Phys. Lett. B368 (1996) 137.

    ADS  MathSciNet  Google Scholar 

  18. S. Chandrasekharan, Nucl. Phys. Proc. Suppl. 42 (1995) 475; S. Chandrasekharan and N. Christ, Nucl. Phys. Proc. Suppl. 42 (1996) 527; N. Christ, Lattice 1996.

    Article  ADS  Google Scholar 

  19. T. Kalkreuter, Phys. Lett. B276 (1992) 485; Phys. Rev. D48 (1993) 1; Comp. Phys. Comm. 95 (1996) 1.

    ADS  MathSciNet  Google Scholar 

  20. M.E. Berbenni-Bitsch, S. Meyer, A. Schäfer, J.J.M. Verbaarschot, and T. Wettig, Microscopic. Universality in the spectrum of the lattice Dirac operator, hep-lat/9704018.

    Google Scholar 

  21. A. Pandey, Ann. Phys. 134 (1981) 119.

    ADS  Google Scholar 

  22. M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. Lett. 74 (1995) 3920.

    Article  ADS  Google Scholar 

  23. M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. Proc. Suppl. 53 (1997) 266.

    Article  ADS  Google Scholar 

  24. T. Guhr, A. Müller-Groeling and H.A. Weidenmüller, Random Matrix Theories in quantum. physics: Common concepts, cond-mat/9707301, Phys. Rep. (in press).

    Google Scholar 

  25. R. Haq, A. Pandey and O. Bohigas, Phys. Rev. Lett. 48 (1982) 1086.

    Article  ADS  Google Scholar 

  26. C. Ellegaard, T. Guhr, K. Lindemann, H.Q. Lorensen, J. Nygard and M. Oxborrow,Phys. Rev. Lett. 75 (1995) 1546.

    Article  ADS  Google Scholar 

  27. S. Deus, P. Koch and L. Sirko, Phys. Rev. E 52 (1995) 1146; H. Gräf, H. Harney, H. Lengeler, C. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt and H.A. Weidenmüller, Phys. Rev. Lett. 69 (1992) 1296.

    ADS  Google Scholar 

  28. T. Ericson, Phys. Rev. Lett. 5 (1960) 430.

    Article  ADS  Google Scholar 

  29. H.A. Weidenmüller, Ann. Phys. (N.Y.) 158 (1984) 78; in Proceedings of T. Ericson’s 60th. birthday.

    Article  Google Scholar 

  30. Y. Imry, Europhysics Lett. 1 (1986) 249; B.L. Altshuler, P.A. Lee and R.A. Webb (eds.), Mesoscopic Phenomena in Solids, North-Holland, New York, 1991; S. Iida, H.A. Weidenmüller and J. Zuk, Phys. Rev. Lett. 64 (1990) 583; Ann. Phys. (N.Y.) 200 (1990), 219; C.W.J. Beenakker, Rev. Mod. Phys. 69 (1997) 731.

    Article  ADS  Google Scholar 

  31. P.W. Anderson, Phys. Rev. 109 (1958) 1492.

    Article  ADS  Google Scholar 

  32. H. Sommers, A. Crisanti, H. Sompolinsky and Y. Stein, Phys. Rev. Lett. 60 (1988) 1895.

    Article  ADS  MathSciNet  Google Scholar 

  33. D. Gross and E. Witten, Phys. Rev. D21 (1980) 446; S. Chandrasekharan, Phys. Lett. B395 (1997) 83.

    ADS  Google Scholar 

  34. P. Di Francesco, P. Ginsparg, and J. Zinn-Justin, Phys. Rep. 254 (1995) 1.

    Article  ADS  Google Scholar 

  35. M. Stephanov, Phys. Rev. Lett. 76 (1996) 4472.

    Article  ADS  Google Scholar 

  36. Y. Fyodorov, B. Khoruzhenko and H. Sommers, Phys. Rev. Lett. 79 (1997) 557.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. C.N. Yang and T.D. Lee, Phys. Rev. 87 (1952) 104, 410.

    Article  ADS  Google Scholar 

  38. V. Matteev and R. Shrock, J. Phys. A: Math. Gen. 28 (1995) 5235.

    Article  ADS  Google Scholar 

  39. J. Vink, Nucl. Phys. B323 (1989) 399.

    Article  ADS  Google Scholar 

  40. I. Barbour, A. Bell, M. Bernaschi, G. Salina and A. Vladikas, Nucl. Phys. B386 (1992) 683.

    Article  ADS  Google Scholar 

  41. J. Osborn and J.J.M. Verbaarschot, in preparation.

    Google Scholar 

  42. A. Smilga and J.J.M. Verbaarschot, Phys. Rev. D51 (1995) 829.

    ADS  MathSciNet  Google Scholar 

  43. M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. D52 (1995) 2563.

    ADS  Google Scholar 

  44. F. Dyson and M. Mehta, J. Math. Phys. 4 (1963) 701.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. M. Mehta, Random Matrices, Academic Press, San Diego, 1991.

    MATH  Google Scholar 

  46. A.M. Odlyzko, Math. Comput. 48 (1987) 273.

    Article  MATH  MathSciNet  Google Scholar 

  47. D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, Am. Math. Soc., Providence RI, 1992.

    MATH  Google Scholar 

  48. G. Hackenbroich and H.A. Weidenmüller, Phys. Rev. Lett. 74 (1995) 4118.

    Article  ADS  Google Scholar 

  49. P. Zinn-Justin, Nucl. Phys. B497 (1997) 725.

    Article  ADS  MathSciNet  Google Scholar 

  50. E. Brézin and S. Hikami, An extension of level spacing universality, cond-mat/9702213.

    Google Scholar 

  51. T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey and S.S.M. Wong, Rev. Mod. Phys. 53 (1981) 385.

    Article  ADS  MathSciNet  Google Scholar 

  52. J.J.M. Verbaarschot and M.R. Zirnbauer, Ann. Phys. (N.Y.) 158 (1984) 78.

    Article  MathSciNet  ADS  Google Scholar 

  53. J.J.M. Verbaarschot, H.A. Weidenmüller and M.R. Zirnbauer, Ann. Phys. (N.Y.) 153 (1984) 367.

    Article  ADS  Google Scholar 

  54. E. Brézin and A. Zee, Nucl. Phys. B453 (1995) 531.

    Article  ADS  Google Scholar 

  55. M. Berry, Proc. Roy. Soc. London A 400 (1985) 229.

    ADS  MATH  MathSciNet  Google Scholar 

  56. E. Brézin and J. Zinn-Justin, Phys. lett. B288 (1992) 54.

    ADS  Google Scholar 

  57. S. Higuchi, C. Itoi, S.M. Nishigaki and N. Sakai, Phys. Lett. B398 (1997) 123.

    ADS  MathSciNet  Google Scholar 

  58. A.V. Andreev, O. Again, B.D. Simons and B.L. Altshuler, Nucl. Phys. B482 (1996) 536.

    Article  ADS  Google Scholar 

  59. A. Altland and M. Zirnbauer, Phys. Rev. Lett. 77 (1996) 4536.

    Article  ADS  Google Scholar 

  60. T. Schäfer and E. Shuryak, Instantons in QCD, hep-ph/9610451, Rev. Mod. Phys. (1997).

    Google Scholar 

  61. D.I. Diakonov and V.Yu. Petrov, Nucl. Phys. B272 (1986) 457.

    Article  ADS  Google Scholar 

  62. J.J.M. Verbaarschot, Phys. Rev. Lett. 72 (1994) 2531; Phys. Lett. B329 (1994) 351.

    Article  ADS  MathSciNet  Google Scholar 

  63. J.J.M. Verbaarschot and I. Zahed, Phys. Rev. Lett. 70 (1993) 3852.

    Article  ADS  Google Scholar 

  64. J.J.M. Verbaarschot, Nucl. Phys. Proc. Suppl. 53 (1997) 88.

    Article  ADS  Google Scholar 

  65. M. Peskin, Nucl. Phys. B175 (1980) 197; S. Dimopoulos, Nucl. Phys. B168 (1980) 69; M. Vysotskii, Y. Kogan and M. Shifman, Sov. J. Nucl. Phys. 42 (1985) 318; D.I. Diakonov and V.Yu. Petrov, Lecture notes in physics, 417, Springer 1993.

    Article  ADS  Google Scholar 

  66. A. Altland, M.R. Zirnbauer, Phys. Rev. Lett. 76 (1996) 3420; Novel Symmetry Classes in. Mesoscopic Normal-Superconducting Hybrid Structures, cond-mat/9602137.

    Article  ADS  Google Scholar 

  67. M.R. Zirnbauer, J. Math. Phys. 37 (1996) 4986; F.J. Dyson, Comm. Math. Phys. 19 (1970) 235.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  68. D. Fox and P. Kahn, Phys. Rev. 134 (1964) B1152; (1965) 228.

    Article  MathSciNet  Google Scholar 

  69. B. Bronk, J. Math. Phys. 6 (1965) 228.

    Article  ADS  Google Scholar 

  70. A.V. Andreev, B.D. Simons, and N. Taniguchi, Nucl. Phys B432 [FS] (1994) 487.

    Article  ADS  MathSciNet  Google Scholar 

  71. F. Dyson, J. Math. Phys. 13 (1972) 90.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  72. G. Mahoux and M. Mehta, J. Phys. I Prance I (1991) 1093.

    MathSciNet  ADS  Google Scholar 

  73. T. Nagao and M. Wadati, J. Phys. Soc. Japan 60 (1991) 2998; J. Phys. Soc. Jap. 60 (1991) 3298; J. Phys. Soc. Jap. bf 61 (1992) 78; J. Phys. Soc. Jap. bf 61 (1992) 1910. 61 (1992) 78, 1910.

    MathSciNet  ADS  Google Scholar 

  74. J.J.M. Verbaarschot, Nucl. Phys. B426 (1994) 559.

    Article  ADS  MathSciNet  Google Scholar 

  75. T. Nagao and P.J. Forrester, Nucl. Phys. B435 (1995) 401.

    Article  ADS  MathSciNet  Google Scholar 

  76. A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Phys. Lett. B 387 (1996) 355.

    ADS  MathSciNet  Google Scholar 

  77. A.D. Jackson and J.J.M. Verbaarschot, Phys. Rev. D53 (1996) 7223.

    ADS  Google Scholar 

  78. M. Stephanov, Phys. Lett. B275 (1996) 249; Nucl. Phys. Proc. Suppl. 53 (1997) 469.

    ADS  Google Scholar 

  79. T. Guhr, J. Math. Phys. 32 (1991) 336.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  80. C. Tracy and H. Widom, Comm. Math. Phys. 161 (1994) 289.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  81. D. Hofstadter, Phys. Rev. B14 (1976) 2239.

    ADS  Google Scholar 

  82. K. Slevin and T. Nagao, Phys. Rev. Lett. 70 (1993) 635.

    Article  ADS  Google Scholar 

  83. J. Kelner and J.J.M. Verbaarschot, in preparation.

    Google Scholar 

  84. J. Osborn and J.J.M. Verbaarschot, in progress.

    Google Scholar 

  85. S. Hands and M. Teper, Nucl. Phys. B347 (1990) 819.

    Article  ADS  Google Scholar 

  86. J. Cullum and R.A. Willoughby, J. Comp. Phys. 44 (1981) 329.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  87. J.J.M. Verbaarschot, Nucl. Phys. B427 (1994) 534.

    Article  ADS  MathSciNet  Google Scholar 

  88. T. Wettig, T. Guhr, A. Schäfer and H. Weidenmüller, The chiral phase transition, random matrix. models, and lattice data, hep-ph/9701387.

    Google Scholar 

  89. P. Forrester, Nucl. Phys. B[FS]402 (1993) 709.

    Article  ADS  MathSciNet  Google Scholar 

  90. T. Wettig, private communication 1997.

    Google Scholar 

  91. T. Jolicoeur and A. Morel, Nucl. Phys. B262 (1985) 627.

    Article  ADS  Google Scholar 

  92. M. Göckeler, R. Horsley, E. Laermann, P. Rakow, G. Schierholtz, R. Sommer and U.-J. Wiese, Nucl. Phys. B334 (1990) 527.

    Article  ADS  Google Scholar 

  93. T. Wettig, A. Schäfer and H. Weidenmüller, Phys. Lett. B367 (1996) 28.

    ADS  Google Scholar 

  94. M.A. Halasz, A.D. Jackson and J.J.M. Verbaarschot, Phys. Lett. B395 (1997) 293; Fermion. determinants in matrix models of QCD at nonzero chemical potential, hep-lat/9703006, Phys. Rev. D (in press).

    ADS  MathSciNet  Google Scholar 

  95. J. Feinberg and A. Zee, Non-Hermitean Random Matrix Theory: method of hermitization, cond-mat/9703118; Nongaussian nonhermitean random matrix theory: phase transition and addition. formalism, cond-mat/9704191; Nonhermitean random matrix theory: method of hermitean reduction, cond-mat/9703087.

    Google Scholar 

  96. K. Efetov, Adv. Phys. 32, 53 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  97. J.J.M. Verbaarschot, H.A. Weidenmüller, and M.R. Zirnbauer, Phys. Rep. 129, 367 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  98. Y. Fyodorov and H. Sommers, JETP Lett. 63 (1996), 1026.

    Article  ADS  Google Scholar 

  99. B. Khoruzhenko, J. Phys. A: Math. Gen. 29, L165 (1996).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  100. Y. Fyodorov, B. Khoruzhenko and H. Sommers, Phys. Lett. A 226, 46 (1997).

    ADS  MathSciNet  Google Scholar 

  101. K. Efetov, Phys. Rev. Lett. 79 (1997) 491; Quantum disordered systems with a direction, cond-mat/9706055.

    Article  ADS  Google Scholar 

  102. V.L. Girko, Theory of random determinants, Kluwer Academic Publishers, Dordrecht, 1990.

    Google Scholar 

  103. M.A. Nowak, New developments in nonhermitean random matrix models, hep-ph/9708418.

    Google Scholar 

  104. J.J.M. Verbaarschot and M.R. Zirnbauer, J. Phys. A17 (1985) 1093.

    ADS  MathSciNet  Google Scholar 

  105. I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut and M.-P. Lombardo, Results on. Finite Density QCD, hep-lat/9705042.

    Google Scholar 

  106. I. Barbour, N. Behihil, E. Dagotto, F. Karsch, A. Moreo, M. Stone and H. Wyld, Nucl. Phys. B275 (1986) 296; M.-P. Lombardo, J.B. Kogut and D.K. Sinclair, Phys. Rev. D54 (1996) 2303.

    Article  ADS  Google Scholar 

  107. I.M. Barbour, S. Morrison and J. Kogut, Lattice gauge theory simulation at nonzero chemical. potential in the chiral limit, hep-lat/9612012.

    Google Scholar 

  108. M. Stephanov, private communication.

    Google Scholar 

  109. E. Dagotto, F. Karsch and A. Moreo, Phys. Lett. 169 B, 421 (1986).

    ADS  Google Scholar 

  110. M.A. Halasz, J. Osborn and J.J.M. Verbaarschot, Random matrix triality at nonzero chemical. potential, hep-lat/9704007, Phys. Rev. D (in press).

    Google Scholar 

  111. Th. Schäfer, Instantons and the Chiral Phase Transition at non-zero Baryon Density, hepph/9708256.

    Google Scholar 

  112. C. Baillie, K.C. Bowler, P.E. Gibbs, I.M. Berbour and M. Rafique, Phys. Lett. 197B, 195 (1987).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Verbaarschot, J. (2002). Universal Behavior in Dirac Spectra. In: van Baal, P. (eds) Confinement, Duality, and Non-Perturbative Aspects of QCD. NATO Science Series: B:, vol 368. Springer, Boston, MA. https://doi.org/10.1007/0-306-47056-X_12

Download citation

  • DOI: https://doi.org/10.1007/0-306-47056-X_12

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-45826-2

  • Online ISBN: 978-0-306-47056-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics