Non-Hermitian random matrix models: Free random variable approach

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 4, 1997, Pages 4100-4106

  Janik, Romuald A ^a   Nowak, Maciej A ^a,b,c   Papp, Gábor ^b,d   Wambach, Jochen ^c   Zahed, Ismail ^e  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b GSI HELMHOLTZZENTRUM FÜR SCHWERIONENFORSCHUNG GMBH   (Germany)

^c DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^d EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^e STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001032742     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.4100     Document Type: Article

References (34)

1. P. Grangé, H.A. Weidenmüller and G. Wolschin, Ann. Phys. (N.Y.)136, 190 (1981);
2. H.A. Weidenmüller, Ann. Phys. (N.Y.)158, 120 (1984).
3. O. Bohigas, Random Matrix Theories and Chaotic Dynamics, Les Houches Lectures (North-Holland, Amsterdam, 1991), and references therein.
4. V.B. Pavlov-Verekin, Phys. Lett. A129, 168 (1988);
5. F M. Dittes, H.L. Harney and I. Rotter, Phys. Lett. A153, 451 (1991).
6. M. Stephanov, Phys. Rev. Lett.76, 137 (1996);
7. R A. Janik, M A. Nowak, G. Papp and I. Zahed, Phys. Rev. Lett.77, 4876 (1996);
8. M A. Halasz, A. Jackson, J.J.M. Verbaarschot (unpublished).
9. V V. Sokolov and V G. Zelevinsky, Phys. Lett. B202, 10 (1988);
10. V V. Sokolov and V G. Zelevinsky, Nucl. Phys. A504, 562 (1989).
11. J.J.M. Verbaarschot, H.A. Weidenmüller and M R. Zirnbauer, Phys. Rep.129, 367 (1985).
12. F. Haake, F. Izrailev, N. Lehmann, D. Saher and H.-J. Sommers, Z. Phys. B88, 359 (1992).
13. N. Lehmann, D. Saher, V V. Sokolov and H.-J. Sommers, Nucl. Phys. A582, 223 (1995).
14. N. Lehmann, D.V. Savin, V.V. Sokolov, and H.-J. Sommers, chao-dyn/9501018.
15. Y V. Fyodorov and H.-J. Sommers, Pis'ma Zh. Éksp. Teor. Fiz.63, 970 (1996) [JETP Lett. 63, 1026 (1996)];
16. Y.V Fyodorov and H.-J. Sommers, J. Math. Phys. (to be published).
17. Y V. Fyodorov, B. Khoruzhenko, and H.-J. Sommers (unpublished).
18. D V. Voiculescu, K J. Dykema, and A. Nica, Free Random Variables (American Mathematical Society, Province, RI, 1992).
19. A. Zee, Nucl. Phys. B474, 726 (1996).
20. J. Ginibre, J. Math. Phys.6, 440 (1965);
21. see also, V.L. Girko, Spectral Theory of Random Matrices (Nauka, Moscow, 1988) (in Russian).
22. C. Mahaux and H.A. Weidenmüller, Shell-model Approach to Nuclear Reactions (North-Holland, Amsterdam, 1969).
23. W. Weisskopf and E. Wigner, Z. Phys.63, 54 (1930) (in German).
24. H.-J. Sommers, A. Crisanti, H. Sompolinsky and Y. Stein, Phys. Rev. Lett.60, 1895 (1988).
25. S. Droz-dotdz-dot, A. Trellakis and J. Wambach, Phys. Rev. Lett.76, 4891 (1996).
26. See, e.g., C.E. Porter, Statistical Theories of Spectra: Fluctuations (Academic, New York, 1965); M.L. Mehta, Random Matrices (Academic, New York, 1991).
27. D V. Voiculescu, Invent. Math.104, 201 (1991).
28. A. Crisanti and H. Sompolinsky, Phys. Rev. A36, 4922 (1987);
29. M. Opper, Europhys. Lett.8, 389 (1989).
30. M A. Nowak, G. Papp and I. Zahed, Phys. Lett. B389, 137 (1996);
31. M A. Nowak, G. Papp and I. Zahed, Phys. Lett. B389, 341 (1996);
32. J. Jurkiewicz, M A. Nowak and I. Zahed, Nucl. Phys. B478, 605 (1996).
33. L A. Pastur, Theor. Math. Phys. (USSR)10, 67 (1972).
34. R A. Janik, M A. Nowak, G. Papp, and I. Zahed, GSI Report No. cond-mat/9612240, 1996 (unpublished).