Gaussian ensemble of tridiagonal symmetric random matrices

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 232, Issue 1-2, 1997, Pages 91-98

  Vagov, A V ^a,b   Vorov, O K ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Exact solution; Toda equations; Tridiagonal random matrices

Indexed keywords

CORRELATORS; DEGREES OF FREEDOM (MECHANICS);

EIGENVALUE PROBLEM; EXACT SOLUTION; MULTIDIMENSIONAL INTEGRAL; RANDOM MATRICES; ROTATIONAL DEGREES OF FREEDOM; ROTATIONAL VARIABLE; SPECTRAL STATISTICS; TODA EQUATIONS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0041163092     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(97)00342-3     Document Type: Article

References (34)

1. O. Bohigas and M.J. Giannoni, in: Lecture notes in physics, Vol. 209, Mathematical and computational methods in nuclear physics, eds. J.S. Denesa, G.M. Gomez and A. Polls (Springer, Berlin, 1984).
2. C.E. Porter, ed., statistical theories of spectra: fluctuations (Academic Press, New York, 1965); M.L. Mehta, Random matrices (Academic Press, New York, 1991).
3. C.E. Porter, ed., statistical theories of spectra: fluctuations (Academic Press, New York, 1965); M.L. Mehta, Random matrices (Academic Press, New York, 1991).
4. J.M. Ziman, Models of disorder (Cambridge Univ. Press, Cambridge, 1990).
5. K. Ishii, Suppl. Prog. Theor. Phys. 53 (1972) 77; S. Alexander, J. Bernasconi, W.R. Schneider and R. Orbach, Rev. Mod. Phys. 53 (1981) 175; P.V. Mieghem, Rev. Mod. Phys. 64 (1992) 755.
6. K. Ishii, Suppl. Prog. Theor. Phys. 53 (1972) 77; S. Alexander, J. Bernasconi, W.R. Schneider and R. Orbach, Rev. Mod. Phys. 53 (1981) 175; P.V. Mieghem, Rev. Mod. Phys. 64 (1992) 755.
7. K. Ishii, Suppl. Prog. Theor. Phys. 53 (1972) 77; S. Alexander, J. Bernasconi, W.R. Schneider and R. Orbach, Rev. Mod. Phys. 53 (1981) 175; P.V. Mieghem, Rev. Mod. Phys. 64 (1992) 755.
8. I.M. Lifshits, S.A. Gredeskul and L.A. Pastur, Introduction of the theory of disordered solids (Wiley-Interscience, New York, 1987).
9. S. Fishman, D.R. Grempel and R.E. Prange, Phys. Rev. Lett. 49 (1982) 509; F.M. Izrailev, Phys. Rep. 129 (1990) 299.
10. S. Fishman, D.R. Grempel and R.E. Prange, Phys. Rev. Lett. 49 (1982) 509; F.M. Izrailev, Phys. Rep. 129 (1990) 299.
11. E.P. Wigner, Proc. Cambridge Philos. Soc. 47 (1951) 790; in: Canadian Math. Congress Proc. (Univ. Toronto Press, Toronto, Canada, 1957).
12. E.P. Wigner, Proc. Cambridge Philos. Soc. 47 (1951) 790; in: Canadian Math. Congress Proc. (Univ. Toronto Press, Toronto, Canada, 1957).
13. E.P. Wigner, Ann. Math. 62 (1955) 548; 65 (1957) 203.
14. E.P. Wigner, Ann. Math. 62 (1955) 548; 65 (1957) 203.
15. Y.V. Fyodorov and A.D. Mirlin, Int. J. Mod. Phys. 8 (1994) 3795, and references therein.
16. S. Iida, H.A. Weindenmuller and J.A. Zuk, Ann. Phys. 200 (1990) 219; D.L. Shepelyansky, Phys. Rev. Lett. 73 (1994) 2607.
17. S. Iida, H.A. Weindenmuller and J.A. Zuk, Ann. Phys. 200 (1990) 219; D.L. Shepelyansky, Phys. Rev. Lett. 73 (1994) 2607.
18. O. Vorov and A. Vagov, Phys. Lett. A 205 (1995) 301; A. Vagov and O. Vorov, unpublished.
19. O. Vorov and A. Vagov, Phys. Lett. A 205 (1995) 301; A. Vagov and O. Vorov, unpublished.
20. M. Toda, J. Phys. Soc. Jpn. 22 (1967) 431.
21. F.J. Dyson, Phys. Rev. 92 (1953) 1331; P.W. Anderson, Phys. Rev. 109 (1957) 1492; B. Derrida and E. Gardner, J. Phys. (Paris) 45 (1984) 1283; E. Gardner, C. Itzykson and B. Derrida, J. Phys. A 17 (1984) 1093; A. Mielke and F. Wegner, Z. Phys. B 62 (1985) 1.
22. F.J. Dyson, Phys. Rev. 92 (1953) 1331; P.W. Anderson, Phys. Rev. 109 (1957) 1492; B. Derrida and E. Gardner, J. Phys. (Paris) 45 (1984) 1283; E. Gardner, C. Itzykson and B. Derrida, J. Phys. A 17 (1984) 1093; A. Mielke and F. Wegner, Z. Phys. B 62 (1985) 1.
23. F.J. Dyson, Phys. Rev. 92 (1953) 1331; P.W. Anderson, Phys. Rev. 109 (1957) 1492; B. Derrida and E. Gardner, J. Phys. (Paris) 45 (1984) 1283; E. Gardner, C. Itzykson and B. Derrida, J. Phys. A 17 (1984) 1093; A. Mielke and F. Wegner, Z. Phys. B 62 (1985) 1.
24. F.J. Dyson, Phys. Rev. 92 (1953) 1331; P.W. Anderson, Phys. Rev. 109 (1957) 1492; B. Derrida and E. Gardner, J. Phys. (Paris) 45 (1984) 1283; E. Gardner, C. Itzykson and B. Derrida, J. Phys. A 17 (1984) 1093; A. Mielke and F. Wegner, Z. Phys. B 62 (1985) 1.
25. F.J. Dyson, Phys. Rev. 92 (1953) 1331; P.W. Anderson, Phys. Rev. 109 (1957) 1492; B. Derrida and E. Gardner, J. Phys. (Paris) 45 (1984) 1283; E. Gardner, C. Itzykson and B. Derrida, J. Phys. A 17 (1984) 1093; A. Mielke and F. Wegner, Z. Phys. B 62 (1985) 1.
26. P. Lloyd, J. Phys. C Ser. 2, Vol. 2 (1969) 1717.
27. M. Toda, in: Theory of nonlinear lattices, eds. M. Cardona, P. Fulde and H.-J. Queisser (Springer, Berlin, 1981).
28. H. Flaschka, Phys. Rev. B 9 (1974) 1924; Prog. Theor. Phys. 51 (1974) 703.
29. H. Flaschka, Phys. Rev. B 9 (1974) 1924; Prog. Theor. Phys. 51 (1974) 703.
30. H. Flashka and D.W. McLaughlin, in: Proc. of Workshop on Contact transformations, Vanderbildt University, Nashville (1974); D.W. McLaughlin, J. Math. Phys. 16 (1975) 96; erratum ibid.; H. Flashka and D.W. McLaughlin, Prog. Theor. Phys. 55 (1976) 438.
31. H. Flashka and D.W. McLaughlin, in: Proc. of Workshop on Contact transformations, Vanderbildt University, Nashville (1974); D.W. McLaughlin, J. Math. Phys. 16 (1975) 96; erratum ibid.; H. Flashka and D.W. McLaughlin, Prog. Theor. Phys. 55 (1976) 438.
32. H. Flashka and D.W. McLaughlin, in: Proc. of Workshop on Contact transformations, Vanderbildt University, Nashville (1974); D.W. McLaughlin, J. Math. Phys. 16 (1975) 96; erratum ibid.; H. Flashka and D.W. McLaughlin, Prog. Theor. Phys. 55 (1976) 438.
33. P.D. Lax, Comm. Pure Appl. Math. 21 (1968) 467.
34. L.D. Landau and E.M. Lifshits, Course of theoretical physics, Vol. 1. Mechanics (Pergamon Press, Oxford, 1960).