Parametric statistics of the scattering matrix: From metallic to insulating quasi-unidimensional disordered systems

Journal de Physique II

Volumn 7, Issue 10, 1997, Pages 1267-1296

  Mucciolo, Eduardo R ^b   Jalabert, Rodolfo A ^a,d   Pichard, Jean Louis ^c  

^a CP 38071   (Brazil)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITÉ DE STRASBOURG   (France)

^d SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOYS; BROWNIAN MOVEMENT; CORRELATION METHODS; ELECTRIC INSULATING MATERIALS; ELECTRIC RESISTANCE; ELECTRON ENERGY LEVELS; ELECTRON SCATTERING; ELECTRON TUNNELING; MATRIX ALGEBRA; METALS; PHASE SHIFT;

DISORDERED SYSTEMS; LOW DIMENSIONAL STRUCTURES;

ELECTRON TRANSPORT PROPERTIES;

EID: 0031250327     PISSN: 11554312     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (80)

1. Efetov K.B., Adv. Phys. 32 (1983) 53.
2. Altshuler B.L. and Shklovskiï B.I., Zh. Eksp. Tear. Fiz. 91 (1986) 220
3. [Sov. Phys. JETP 64 (1986) 127]
4. Bohigas O., in "Chaos and Quantum Physics" ,M.-J. Giannoni, A. Voros, and J. ZinnJustin, Eds. (North-Holland, New York, 1991).
5. Stone A.D., Mello P.A., Muttalib K.A. and Pichard J.-L., in "Mesoscopic Phenomena in Solids", B.L. Altshuler, P.A. Lee and R.A. Webb, Eds. (North-Holland, Amsterdam, 1991).
6. Beenakker C.W.J., Phys. Rev. B 47 (1993) 15763.
7. Verbaarschot J.J.M., Weidenmüller H.A., and Zirnbauer M.R., Phys. Rep. 129 (1985) 367.
8. lida S., Weidenmüller H.A. and Zuk, Annals Phys. 200 (1990) 219.
9. Baranger H.U. and Mello P.A., Phys. Rev. Lett. 73 (1994) 142.
10. Jalabert R.A., Pichard J.-L. and Beenakker C.W.J., Europhys. Lett. 27 (1994) 255.
11. Pluhär Z., Weidenmüller H.A., Zuk J.A. and Lewenkopf C.H., Phys. Rev. Lett. 73 (1994) 2115;
12. Pluhär Z., Weidenmüller H.A., Zuk J.A., Lewenkopf C.H. and Wegner F.J., Annals Phys. 243 (1995) 1.
13. Jalabert R.A. and Pichard J.-L., J. Phys. France 5 (1995) 287.
14. Notice the typographic mistake in equation (4.5): the confining potential should read V(λ) = [N+(2-β)/β] ln(1+γ).
15. Dyson F.J., J. Math. Phys. 3 (1962) 140.
16. Mehta M.L., Random Matrices, 2nd ed. (Academic Press, San Diego, 1991).
17. Bliimel R. and Smilansky U., Phys. Rev. Lett. 64 (1989) 241.
18. Szafer A. and Altslmler B.L., Phys. Rev. Lett. 70 (1993) 587
19. Simons B.D., Szafer A. and Altshuler B.L., Pis'ma Zh. Eksp. Tear. Fiz. 57 (1993) 268 [
20. JETP Lett. 57 (1993) 276 ].
21. Simons B.D. and Altshuler B.L., Phys. Rev. Lett. 70 (1993) 4063;
22. Phys. Rev. B 48 (1993) 5422.
23. Faas M., Simons B.D., Zotos X. and Altshuler B.L., Phys. Rev. B 48 (1993) 5439.
24. Mucciolo E.R., Capaz R.B., Altshuler B.L. and Joannopoulos J.D., Phys. Rev. B 50 (1994) 8245.
25. Simons B.D., Hashimoto A., Courtney M., Kleppner D. and Altshuler B.L., Phys. Rev. Lett. 71 (1993) 2899.
26. Dietz B., Lombardi M. and Seligman T.H., Phys. Lett. A 215 (1996) 181.
27. Lehmann N., Savin D.V., Sokolov V.V. and Sommers H.-J., Physica D 86 (1995) 572.
28. Fyodorov Y.V. and Sommers H.-J., Phys. Rev. Lett. 76 (1996) 4709;
29. J. Math. Phys. 38 (1997) 1918.
30. Fyodorov Y.V., Savin D.V. and Sommers H.-J., Phys. Rev. E 55 (1997) 4857.
31. Gopar V.A., Mello P.A. and Büttiker M., Phys. Rev. Lett. 77 (1996) 3005.
32. Smith F.T., Phys. Rev. 118 (1960) 349; 119 (1960) 2098.
33. Fisher D.S. and Lee P.A., Phys. Rev. B 23 (1981) 6851.
34. Lee P.A. and Fisher D.S., Phys. Rev. Lett. 47 (1981) 882.
35. Baranger H.U., DiVincenzo O.P., Jalabert R.A. and Stone A.D., Phys. Rev. B 44 (1991) 10637.
36. Landauer R., Philos. Mag. 21 (1970) 863;
37. Büttiker M., Phys. Rev. Lett. 57 (1986) 1761.
38. Muzykantskii B.A. and Khmelnitskii D.E., Phys. Rev. B 51 (1995) 5480.
39. 2 were drawn from the proper Gaussian ensemble. The averages were performed over the 100 central eigenvalues and 50 realizations.
40. Simons B.D., Lee P.A. and Altshuler B.L., Phys. Rev. Lett. 72 (1994) 64;
41. Nucl. Phys B 409 (1993) 487.
42. Andreev A.V., Agam O., Simons B.D. and Altshuler B.L., Phys. Rev. Lett. 76 (1996) 3947.
43. Macêdo A.M.S., Phys. Rev. E 50 (1994) R659.
44. Beenakker C.W.J., Phys. Rev. Lett. 70 (1993) 4126.
45. Dyson F.J., J. Math. Phys. 3 (1962) 1191.
46. Pandey A. and Shukla P., J. Phys. A 24 (1991) 3907
47. Pandey A., Ramaswamy R. and Shukla P., Pramana J. Phys. (India) 41 (1993) L75.
48. Rau J., Phys. Rev. B 51 (1995) 7734.
49. Frahm K. and Pichard J.-L., J. Phys. I France 5 (1995) 847; 5 (1995) 877.
50. Sutherland B., Phys. Rev. A 4 (1971) 2019;
51. 5 (1972) 1372.
52. For a solution for the case of Hamiltonian eigenvalues when γ= 2, see Beenakker C.W.J. and Rejaei B., Physica A 203 (1994) 60.
53. Dyson F.J., J. Math. Phys. 13 (1972) 90.
54. Akkermans E. and Montambaux G., Phys. Rev. Lett. 68 (1992) 642.
55. Blümel R. and Smilansky U., Phys. Rev. Lett. 60 (1988) 477;
56. Physica D 36 (1989) 111.
57. Baranger H.U., Jalabert R.A. and Stone A.D., Chaos 3 (1993) 665.
58. Eckhardt B., Chaos 3 (1993) 613.
59. Lewenkopf C.H. and Weidenmüller H.A., Ann. Phys. (N.Y.) 212 (1991) 53.
60. Doron E. and Smilansky U., Phys. Rev. Lett. 68 (1992) 1255;
61. Nonlinearity 5 (1992) 1055.
62. Lee P.A., Stone A.D. and Fukuyama H., Phys. Rev. B 35 (1987) 1039.
63. Lane A.M. and Thomas R.G., Rev. Mod. Phys. 30 (1958) 257.
64. Mahaux C. and Weidenmüller H.A., Shell-Model Approach to Nuclear Reactions (NorthHolland, Amsterdam, 1969).
65. We remark that even though equation (3.3) was obtained from the approximate equation (3.1), it is of more general validity (see discussion in Ref. [22]). Equation (3.2), however, is only correct in the resonant regime.
66. Avishai Y.G., Pichard J.-L. and Muttalib K.A., J. Phys. I France 3 (1993) 2343.
67. Pichard J.-L., in "Quantum Coherence in Mesoscopic Systems", B. Kramer, Ed., NATO ASI Series B 254 (Plenum, New York, 1991).
68. Ladieu F., Mailly D. and Sanquer M., J. Phys. I France 3 (1993) 2321.
69. Poirier W., Sanquer M. and Mailly D., in "Hopping and Related Phenomena VI" (Jerusalem, 1995).
70. Schulz H.J., in "Mesoscopic Quantum Physics", E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin, Eds. (Elsevier, Amsterdam, 1995).
71. Kane C.L. and Fisher M.P.A., Phys. Rev. B 46 (1992) 15233.
72. Shepelyansky D.L., Phys. Rev. Lett. 73 (1994) 2067.
73. Weinman D., Miiller-Groeling A., Pichard J.-L., and Frahm K., Phys. Rev. Lett. 75 (1995) 1598.
74. von Oppén F., Wettig T. and Müller J., Phys. Rev. Lett. 75 (1995) 1598.
75. Dalian R., Nuovo Cim. B 57 (1968) 183.
76. Mello P.A., private communication.
77. Ullah N. and Porter C.E., Phys. Lett. 6 (1963) 301.
78. Mello P.A., J. Phys. A 23 (1990) 4061.
79. Ozorio de Almeida A.M., Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, 1988).
80. Brouwer P.W., Frahm K.M. and Beenakker C.W.J., unpublished.