Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 4 2, 2003, Pages 461041-4610413

  Garcia Garcia A M ^a   Verbaarschot, J J M ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; CORRELATION METHODS; EIGENVALUES AND EIGENFUNCTIONS; FRACTALS; HAMILTONIANS; INTERPOLATION;

RANDOM MATRIX ENSEMBLES (RME);

QUANTUM THEORY;

EID: 0038542273     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (76)

1. V. Kravtsov and K. Muttalib, Phys. Rev. Lett. 79, 1913 (1997).
2. M. Moshe, H. Neuberger, and B. Shapiro, Phys. Rev. Lett. 73, 1497 (1994).
3. A.D. Mirlin, Y.V. Fyodorov, F.M. Dittes, J. Quezada, and T.H. Seligman, Phys. Rev. E 54, 3221 (1996).
4. K.A. Muttalib, Y. Chen, M.B.H. Ismail, and V.N. Nicopoulos, Phys. Rev. Lett. 71, 471 (1993).
5. A. Mirlin, Phys. Rep. 326, 259 (2000); M. Janssen, ibid. 295, 1 (1998).
6. A. Mirlin, Phys. Rep. 326, 259 (2000); M. Janssen, ibid. 295, 1 (1998).
7. E. Bogomolny, O. Bohigas, and M.P. Pato, Phys. Rev. E 55, 6707 (1997).
8. A.M. García-García and J.J.M. Verbaarschot, Nucl. Phys. B 586, 668 (2000).
9. C. Blecken, Y. Chen, and K.A. Muttlalib, J. Phys. A. 27, L563 (1994).
10. B.I. Shklovskii, B. Shapiro, B.R. Sears, P. Lambrianides, and H.B. Shore, Phys. Rev. B 47, 11 487 (1993).
11. S. Nishigaki, Phys. Rev. E 59, 2853 (1999).
12. C.-M. Ho and J.T. Chalker, Phys. Rev. B 54, 8708 (1996); J.-S. Caux, N. Taniguchi, and A.M. Tsvelik, Nucl. Phys. B 525, 671 (1998).
13. C.-M. Ho and J.T. Chalker, Phys. Rev. B 54, 8708 (1996); J.-S. Caux, N. Taniguchi, and A.M. Tsvelik, Nucl. Phys. B 525, 671 (1998).
14. R. Klesse and M. Metzler, Phys. Rev. Lett. 79, 721 (1997).
15. J.C. Osborn and J.J.M. Verbaarschot, Phys. Rev. Lett. 81, 268 (1998); Nucl. Phys. B 525, 738 (1998).
16. J.C. Osborn and J.J.M. Verbaarschot, Phys. Rev. Lett. 81, 268 (1998); Nucl. Phys. B 525, 738 (1998).
17. C.M. Canali and V.E. Kravtsov, Phys. Rev. E 51, R5185 (2000).
18. A.M. García-García, Phys. Rev. E 64, 066121 (2001).
19. V.E. Kravtsov and A.M. Tsvelik, Phys. Rev. B 62, 9888 (2000).
20. E.B. Bogomolny, U. Gerland, and C. Schmidt, Phys. Rev. E 59, R1315 (1999).
21. M.R. Zirnbauer and F.D.M. Haldane, Phys. Rev. B 52, 8729 (1995).
22. B. Sutherland, J. Math. Phys. 12, 246 (1971); 12, 251 (1971).
23. B. Sutherland, J. Math. Phys. 12, 246 (1971); 12, 251 (1971).
24. F. Calogero, J. Math. Phys. 10, 2191 (1969); 10, 2197 (1969); 12, 419 (1971).
25. F. Calogero, J. Math. Phys. 10, 2191 (1969); 10, 2197 (1969); 12, 419 (1971).
26. F. Calogero, J. Math. Phys. 10, 2191 (1969); 10, 2197 (1969); 12, 419 (1971).
27. Y. Chen and K. Muttalib, J. Phys.: Condens. Matter 6, L293 (1994).
28. T.H. Baker and P.J. Forrester, Commun. Math. Phys. 188, 175 (1997).
29. A. Altland and M. Zirnbauer, Phys. Rev. B 55, 1142 (1997).
30. M.A. Olshannetsky and A.M. Perelomov, Phys. Rep. 94, 313 (1983).
31. B. Sutherland, Phys. Rev. A 4, 2019 (1971).
32. P.J. Forrester, Nucl. Phys. B 416, 377 (1994).
33. Z.N.C. Ha, Phys. Rev. Lett. 73, 1574 (1994); Nucl. Phys. B 435, 604 (1995).
34. Z.N.C. Ha, Phys. Rev. Lett. 73, 1574 (1994); Nucl. Phys. B 435, 604 (1995).
35. F. Lesage, V. Pasquier, and D. Serban, Nucl. Phys. B 435, 585 (1995).
36. R.P. Stanley, Adv. Math. 77, 76 (1989).
37. R.J. Muirhead, Aspects of Multivariate Statistical Theory (Wiley, New York, 1982).
38. H. Ujino, M. Wadati, J. Phys. Soc. Jpn. 65, 653 (1996).
39. T. Guhr and H. Kohler, e-print math-ph/0011007.
40. F.D. Haldane, Phys. Rev. Lett. 67, 937 (1991).
41. Z. Yan, Contemp. Math. 138, 239 (1992).
42. N. Kawakami and S. Yang, Phys. Rev. Lett. 67, 2493 (1991).
43. J. Chalker, V. Kravtsov, and I. Lerner, JETP Lett. 64, 386 (1996).
44. J. Chalker, I. Lerner, and R. Smith, Phys. Rev. Lett. 77, 554 (1996).
45. J.L. Cardy, Nucl. Phys. B: Field Theory Stat. Syst. 270, 186 (1986).
46. A.D. Mironov and Z.V. Zabrodin, Phys. Rev. Lett. 66, 534 (1991).
47. A.D. Mironov and Z.V. Zabrodin, Int. J. Mod. Phys. A 7, 3885 (1992).
48. D. Senechal, e-print cond-mat/9908262.
49. C.N. Yang and C.P. Yang, J. Math. Phys. 10, 1115 (1969).
50. Y.V. Fyodorov and A. Mirlin, Phys. Rev. B 55, R16001 (1997).
51. V. Kravtsov, e-print cond-mat/9603166.
52. O. Bohigas, M.J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
53. J.J.M. Verbaarschot, H.A. Weidenmueller, and M.R. Zirnbauer, Phys. Rep. 129, 367 (1985).
54. T. Guhr and H. Weidenmueller, Ann. Phys. (Leipzig) 193, 472 (1989).
55. Weak Chaos and Quasi Regular Patterns, edited by G.M. Zaslavsky et al. (Cambridge University Press, Cambridge, 1991).
56. W. Li and P. Bak, Phys. Rev. Lett. 57, 655 (1986).
57. G. Casati and T. Prosen, Phys. Rev. E 59, R2516 (1999); F. Borgonovi, G. Casati, and B. Li, Phys. Rev. Lett. 77, 4744 (1996).
58. G. Casati and T. Prosen, Phys. Rev. E 59, R2516 (1999); F. Borgonovi, G. Casati, and B. Li, Phys. Rev. Lett. 77, 4744 (1996).
59. W. Kohn and J.M. Luttinger, Phys. Rev. 96, 1488 (1954).
60. A.K. Ramdas and S. Rodriguez, Rep. Prog. Phys. 44, 1297 (1981).
61. D. Wintgen and H. Marxer, Phys. Rev. Lett. 60, 971 (1988).
62. G. Tanner, P. Scherer, E.B. Bogomolny, B. Eckhardt, and D. Wintgen, Phys. Rev. Lett. 67, 2410 (1991).
63. B. Hu, B. Li, J. Liu, and Y. Gu, Phys. Rev. Lett. 82, 4224 (1999).
64. T.M. Fromhold, Phys. Rev. Lett. 87, 046803 (2001).
65. F.J. Dyson, J. Math. Phys. 4, 701 (1963).
66. M.L. Mehta, Random Matrices, 2nd ed. (Academic Press, San Diego, 1991).
67. P. Arve, Phys. Rev. A 44, 6920 (1991).
68. R.L. Weaver and D. Sornette, Phys. Rev. E 52, 3341 (1995).
69. B.L. Altshuler and L.S. Levitov, Phys. Rep. 288, 487 (1997).
70. K.M. Frahm et al., Phys. Rev. Lett. 78, 1440 (1997).
71. R. Ketzmerick, Phys. Rev. B 54, 10 841 (1996); A.P. Micolich et al., Phys. Rev. Lett. 87, 036802 (2001); Phys. Rev. B 56, 12 733 (1997).
72. R. Ketzmerick, Phys. Rev. B 54, 10 841 (1996); A.P. Micolich et al., Phys. Rev. Lett. 87, 036802 (2001); Phys. Rev. B 56, 12 733 (1997).
73. R. Ketzmerick, Phys. Rev. B 54, 10 841 (1996); A.P. Micolich et al., Phys. Rev. Lett. 87, 036802 (2001); Phys. Rev. B 56, 12 733 (1997).
74. P.B. Wilkinson et al., Phys. Rev. E 64, 026203 (2001); A. P. Micolich et al., Phys. Rev. Lett. 87, 036802 (2001).
75. P.B. Wilkinson et al., Phys. Rev. E 64, 026203 (2001); A. P. Micolich et al., Phys. Rev. Lett. 87, 036802 (2001).
76. A. Shudo and Y. Shimizu, Phys. Rev. A 42, 6264 (1990).