On correlation functions of characteristic polynomials for chiral Gaussian unitary ensemble

Nuclear Physics B

Volumn 647, Issue 3, 2002, Pages 581-597

  Fyodorov, Yan V ^a   Strahov, Eugene ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037203026     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(02)00904-5     Document Type: Article

References (41)

1. K. Slevin, T. Nagao, Impurity scattering in mesoscopic quantum wires and the Laguerre ensemble, Phys. Rev. B 50 (1994) 2380.
2. J.J.M. Verbaarchot, I. Zahed, Spectral density of the QCD Dirac operator near zero virtuality, Phys. Rev. Lett. 70 (1993) 3852.
3. P.J. Forrester, The spectrum edge of random matrix ensembles, Nucl. Phys. B 402 (1993) 709;
4. T. Nagao, P.J. Forrester, Asymptotic correlations at the spectrum edge of random matrices, Nucl. Phys. B 435 (1995) 401.
5. C. Tracy, H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161 (1994) 289.
6. A.V. Andreev, B.D. Simons, N. Taniguchi, Supersymmetry applied to the spectrum edge of random matrix ensembles, Nucl. Phys. B 432 (1994) 487.
7. A.D. Jackson, M.K. Sener, J.J.M. Verbaarschot, Finite volume partition functions and Itzykson-Zuber integrals, Phys. Lett. B 387 (1996) 355.
8. A.D. Jackson, M.K. Sener, J.J.M. Verbaarschot, Universality near zero virtuality, Nucl. Phys. B 479 (1996) 707.
9. A.D. Jackson, M.K. Sener, J.J.M. Verbaarschot, Universality of correlation functions in random matrix models of QCD, Nucl. Phys. B 506 (1997) 612.
10. T. Guhr, T. Wettig, Universal spectral correlations of the Dirac opearator at finite temperature, Nucl. Phys. B 506 (1997) 589.
11. J. Jurkewich, M.A. Nowak, I. Zahed, Dirac spectrum in QCD and quark masses, Nucl. Phys. B 478 (1996) 605;
12. R.A. Janik, M.A. Nowak, I. Zahed, Chiral random matrix models: thermodynamics, phase transitions and universality, Phys. Lett. B 392 (1997) 155.
13. T.Wilke, T. Guhr, T.Wettig, The microscopic spectrum of the QCD Dirac operator with finite quark masses, Phys. Rev. D 57 (1998) 6486.
14. G. Akemann, P.H. Damgaard, U. Magnea, S.M. Nishigaki, Universality of random matrices in the microscopic limit and the Dirac operator spectrum, Nucl. Phys. B 487 (1997) 721;
15. P.H. Damgaard, S.M. Nishigaki, Universal spectral correlators and massive Dirac operators, Nucl. Phys. B 518 (1998) 495;
16. P.H. Damgaard, S.M. Nishigaki, Universal massive spectral correlators and three-dimensional QCD, Phys. Rev. D 57 (1998) 5299;
17. G. Akemann, Microscopic correlations for non-Hermitian Dirac operators in three-dimensional QCD, Phys. Rev. D 64 (2001) 114021.
18. E. Brezin, S. Hikami, Characteristic polynomials of random matrices, Commun. Math. Phys. 214 (2000) 111.
19. G. Akemann, E. Kanzieper, Spectra of massive and massless QCD Dirac operators: a novel link, Phys. Rev. Lett. 85 (2000) 1174;
20. G. Akemann, E. Kanzieper, Spectra of massive QCD Dirac operators from random matrix theory: all three chiral symmetry breaking patterns, Nucl. Phys. B (Proc. Suppl.) 94 (2001) 681.
21. D. Dalmazi, J.J.M. Verbaarschot, The replica limit of unitary matrix integrals, Nucl. Phys. B 592 (2001) 419.
22. J.J. Verbaarschot, T. Wettig, Random matrix theory and chiral symmetry in QCD, Annu. Rev. Nucl. Part. Sci. 50 (2000) 343.
23. T. Akuzawa, M. Wadati, Effective QCD partition function in sectors with non-zero topological charge and Itzykson-Zuber type integral, J. Phys. Soc. Jpn 67 (1998) 2151.
24. A.V. Andreev, B.D. Simons, Correlator of the spectral determinants in quantum chaos, Phys. Rev. Lett. 75 (1995) 2304.
25. S. Hikami, R. Pnini, Density of state in a complex random matrix theory with external source, J. Phys. A 31 (1998) L587.
26. T. Guhr, T. Wettig, An Itzykson-Zuber-like integral and diffusion for complex ordinary and supermatrices, J. Math. Phys. 37 (12) (1996) 6395;
27. T. Guhr, H. Kohler, Recursive construction for a class of radial functions I: ordinary space, mathph/0011007.
28. C. Itzykson, J.B. Zuber, The planar approximation II, J. Math. Phys. 21 (1980) 411.
29. Harish-Chandra, Differential operators on a semisimple Lie algebra, Proc. Nat. Acad. Sci. 42 (1956) 252.
30. J.J. Duistermaat, G.J. Heckman, On the variation in the co-homology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982) 259;
31. J.J. Duistermaat, G.J. Heckman, Invent. Math. 72 (1983) 153.
32. F.A. Berezin, F.I. Karpelevich, Dokl. Akad. Nauk SSSR 118 (1958) 9.
33. K.B. Efetov, Supersymmetry in Disorder and Chaos, Cambridge Univ. Press, Cambridge, 1997.
34. Y.V. Fyodorov, Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation, Nucl. Phys. B 621 (2002)643, math-ph/0106006.
35. Y.V. Fyodorov, E. Strahov, Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kähler manifolds, Nucl. Phys. B 630 (2002) 453, math-ph/0201045.
36. Y.V. Fyodorov, E. Strahov, An exact formula for general spectral correlation function of random Hermitian matrices, math-ph/0204051.
37. B. Klein, J.J.M. Verbaarschot, Spectral universality of real chiral random matrix ensembles, Nucl. Phys. B 588 (2000) 483.
38. G. Akemann, The solution of a chiral random matrix model with complex eigenvalues, hep-th/0204246;
39. G. Akemann, Microscopic correlation functions for the QCD Dirac operator with chemical potential, hepth/0204068.
40. Y.V. Fyodorov, B.A. Khoruzhenko, Systematic analytical approach to correlation functions of resonances in quantum chaotic scattering, Phys. Rev. Lett. 83 (1999) 65.
41. P. Lancaster, The Theory of Matrices, Academic Press, New York, 1985, p. 185.