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Random-matrix theory of quantum transport

C. W. J. Beenakker

C. W. J. Beenakker

  • Instituut-Lorentz, University of Leiden, 2300 RA Leiden, The Netherlands `

Rev. Mod. Phys. 69, 731 – Published 1 July, 1997

DOI: https://doi.org/10.1103/RevModPhys.69.731

Abstract

This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined region with a chaotic classical dynamics, which is coupled to two electron reservoirs via point contacts. The disordered wire also connects two reservoirs, either directly or via a point contact or tunnel barrier. One of the two reservoirs may be in the superconducting state, in which case conduction involves Andreev reflection at the interface with the superconductor. In the case of the quantum dot, the distribution of the scattering matrix is given by either Dyson’s circular ensemble for ballistic point contacts or the Poisson kernel for point contacts containing a tunnel barrier. In the case of the disordered wire, the distribution of the scattering matrix is obtained from the Dorokhov-Mello-Pereyra-Kumar equation, which is a one-dimensional scaling equation. The equivalence is discussed with the nonlinear σ model, which is a supersymmetric field theory of localization. The distribution of scattering matrices is applied to a variety of physical phenomena, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.

References (432)

  1. Abrahams, E., P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, 1979, Phys. Rev. Lett. 42, 673.
  2. Abrikosov, A. A., 1981, Solid State Commun. 37, 997.
  3. Agraït, N., J. G. Rodrigo, and S. Vieira, 1992, Phys. Rev. B 46, 5814.
  4. Akamann, G., and J. Ambjørn, 1996, J. Phys. A 29, L555.
  5. Aleiner, I. L., and L. I. Glazman, 1996, Phys. Rev. Lett. 77, 2057.
  6. Aleiner, I. L., and A. I. Larkin, 1997, Phys. Rev. E 55, 1243.
  7. Alhassid, Y., and H. Attias, 1996, Phys. Rev. Lett. 76, 1711.
  8. Alhassid, Y., and C. H. Lewenkopf, 1995, Phys. Rev. Lett. 75, 3922.
  9. Allsopp, N. K., J. Sanchez Canizares, R. Raimondi, and C. J. Lambert, 1996, J. Phys., Condens. Matter. 8, L377.
  10. Altland, A., 1991, Z. Phys. B 82, 105.
  11. Altland, A., and M. R. Zirnbauer, 1996, Phys. Rev. Lett. 76, 3420.
  12. Altland, A., and M. R. Zirnbauer, 1997, Phys. Rev. B 55, 1142.
  13. Altshuler, B. L., 1985, Pis'ma Zh. Eksp. Teor. Fiz. 41, 530 [JETP Lett. 41, 648].
  14. Altshuler, B. L., and A. G. Aronov, 1985, in Electron-Electron Interactions in Disordered Systems, edited by A. L. Efros and M. Pollak (North-Holland, Amsterdam), p. 1.
  15. Altshuler, B. L., Y. Gefen, A. Kamenev, and L. S. Levitov, 1997, Phys. Rev. Lett. 78, 2803.
  16. Altshuler, B. L., D. E. Khmel’nitskiĭ, and B. Z. Spivak, 1983, Solid State Commun. 48, 841.
  17. Altshuler, B. L., P. A. Lee, and R. A. Webb, Eds., 1991, Mesoscopic Phenomena in Solids (North-Holland, Amsterdam), p. 1.
  18. Altshuler, B. L., L. S. Levitov, and A. Yu. Yakovets, 1994, Pis'ma Zh. Eksp. Teor. Fiz. 59, 821 [JETP Lett. 59, 857].
  19. Altshuler, B. L., and B. I. Shklovskiĭ, 1986, Zh. Eksp. Teor. Fiz. 91, 220 [Sov. Phys. JETP 64, 127].
  20. Altshuler, B. L., and B. D. Simons, 1995, in Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin (North-Holland, Amsterdam).
  21. Altshuler, B. L., and B. Z. Spivak, 1987, Zh. Eksp. Teor. Fiz. 92, 609 [Sov. Phys. JETP 65, 343].
  22. Ambjørn, J., J. Jurkiewicz, and Yu. M. Makeenko, 1990, Phys. Lett. B 251, 517.
  23. Ambjørn, J., and Yu. M. Makeenko, 1990, Mod. Phys. Lett. A 5, 1753.
  24. Anantram, M. P., and S. Datta, 1996, Phys. Rev. B 53, 16390.
  25. Anderson, P. W., E. Abrahams, and T. V. Ramakrishnan, 1979, Phys. Rev. Lett. 43, 718.
  26. Anderson, P. W., D. J. Thouless, E. Abrahams, and D. S. Fisher, 1980, Phys. Rev. B 22, 3519.
  27. Andreev, A. F., 1964, Zh. Eksp. Teor. Fiz. 46, 1823[Sov. Phys. JETP 19, 1228[.
  28. Andreev, A. F., 1966, Zh. Eksp. Teor. Fiz. 51, 1510 [Sov. Phys. JETP 24, 1019].
  29. Andreev, A. V., O. Agam, B. D. Simons, and B. L. Altshuler, 1996, Phys. Rev. Lett. 76, 394.
  30. Argaman, N., 1995, Phys. Rev. Lett. 75, 2750.
  31. Argaman, N., 1996, Phys. Rev. B 53, 7035.
  32. Argaman, N., 1997, Los Alamos preprint archive, .
  33. Argaman, N., Y. Imry, and U. Smilansky, 1993, Phys. Rev. B 47, 4440.
  34. Argaman, N., and A. Zee, 1996, Phys. Rev. B 54, 7406.
  35. Artemenko, S. N., A. F. Volkov, and A. V. Zaǐtsev, 1979, Solid State Commun. 30, 771.
  36. Ashcroft, N. W., and N. D. Mermin, 1976, Solid State Physics (Holt, Rinehart and Winston, New York).
  37. Averin, D. V., A. N. Korotkov, and K. K. Likharev, 1991, Phys. Rev. B 44, 6199.
  38. Averin, D. V., and K. K. Likharev, 1991, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam), p. 173.
  39. Averin, D. V., and Yu. V. Nazarov, 1990, Phys. Rev. Lett. 65, 2446.
  40. Bakker, S. J. M., E. van der Drift, T. M. Klapwijk, H. M. Jaeger, and S. Radelaar, 1994, Phys. Rev. B 49, 13275.
  41. Balents, L., and M. P. A. Fisher, 1996, Phys. Rev. Lett. 76, 2782.
  42. Balents, L., M. P. A. Fisher, and M. R. Zirnbauer, 1997, Los Alamos preprint archive, .
  43. Balian, R., 1968, Nuovo Cimento B 57, 183.
  44. Baranger, H. U., 1996, in Nano-Science and Technology, edited by G. Timp (American Institute of Physics, New York).
  45. Baranger, H. U., R. A. Jalabert, and A. D. Stone, 1993a, Phys. Rev. Lett. 70, 3876.
  46. Baranger, H. U., R. A. Jalabert, and A. D. Stone, 1993b, CHAOS 3, 665.
  47. Baranger, H. U., and P. A. Mello, 1994, Phys. Rev. Lett. 73, 142.
  48. Baranger, H. U., and P. A. Mello, 1995, Phys. Rev. B 51, 4703.
  49. Baranger, H. U., and P. A. Mello, 1996a, Europhys. Lett. 33, 465.
  50. Baranger, H. U., and P. A. Mello, 1996b, Phys. Rev. B 54, 14297.
  51. Basor, E. L., and C. A. Tracy, 1993, J. Stat. Phys. 73, 415.
  52. Beenakker, C. W. J., 1991, Phys. Rev. B 44, 1646.
  53. Beenakker, C. W. J., 1992a, Phys. Rev. B 46, 12841.
  54. Beenakker, C. W. J., 1992b, in Transport Phenomena in Mesoscopic Systems, edited by H. Fukuyama and T. Ando (Springer, Berlin), p. 235.
  55. Beenakker, C. W. J., 1993a, Phys. Rev. Lett. 70, 1155.
  56. Beenakker, C. W. J., 1993b, Phys. Rev. Lett. 70, 4126.
  57. Beenakker, C. W. J., 1993c, Phys. Rev. B 47, 15763.
  58. Beenakker, C. W. J., 1994a, Nucl. Phys. B 422, 515.
  59. Beenakker, C. W. J., 1994b, Phys. Rev. B 49, 2205.
  60. Beenakker, C. W. J., 1995, in Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin (North-Holland, Amsterdam), p. 279.
  61. Beenakker, C. W. J., and M. Büttiker, 1992, Phys. Rev. B 46, 1889.
  62. Beenakker, C. W. J., and J. A. Melsen, 1994, Phys. Rev. B 50, 2450.
  63. Beenakker, C. W. J., J. A. Melsen, and P. W. Brouwer, 1995, Phys. Rev. B 51, 13883.
  64. Beenakker, C. W. J., J. C. J. Paasschens, and P. W. Brouwer, 1996, Phys. Rev. Lett. 76, 1368.
  65. Beenakker, C. W. J., and B. Rejaei, 1993, Phys. Rev. Lett. 71, 3689.
  66. Beenakker, C. W. J., and B. Rejaei, 1994a, Phys. Rev. B 49, 7499.
  67. Beenakker, C. W. J., and B. Rejaei, 1994b, Physica A 203, 61.
  68. Beenakker, C. W. J., B. Rejaei, and J. A. Melsen, 1994, Phys. Rev. Lett. 72, 2470.
  69. Beenakker, C. W. J., and H. van Houten, 1991, Solid State Phys. 44, 1.
  70. Belitz, D., and T. R. Kirkpatrick, 1994, Rev. Mod. Phys. 66, 261.
  71. Bergmann, G., 1984, Phys. Rep. 107, 1.
  72. Berkovits, R., and S. Feng, 1992, Phys. Rev. B 45, 97.
  73. Berkovits, R., and S. Feng, 1994, Phys. Rep. 238, 135.
  74. Berry, M. V., 1985, Proc. R. Soc. London 400, 229.
  75. Birge, N. O., B. Golding, and W. H. Maemmerle, 1989, Phys. Rev. Lett. 62, 195.
  76. Blonder, G. E., M. Tinkham, and T. M. Klapwijk, 1982, Phys. Rev. B 25, 4515.
  77. Blümel, R., and U. Smilansky, 1988, Phys. Rev. Lett. 60, 477.
  78. Blümel, R., and U. Smilansky, 1990, Phys. Rev. Lett. 64, 241.
  79. Bohigas, O., 1990, in Chaos and Quantum Physics, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam), p. 87.
  80. Bohigas, O., M.-J. Giannoni, A. M. Ozorio de Almeida, and C. Schmit, 1995, Nonlinearity 8, 203.
  81. Bohigas, O., M.-J. Giannoni, and C. Schmit, 1984, Phys. Rev. Lett. 52, 1.
  82. Boutet de Monvel, A., L. Pastur, and M. Shcherbina, 1995, J. Stat. Phys. 79, 585.
  83. Brézin, E., and A. Zee, 1993, Nucl. Phys. B 402, 613.
  84. Brézin, E., and A. Zee, 1994, Phys. Rev. E 49, 2588.
  85. Brezini, A., and N. Zekri, 1992, Phys. Status Solidi B 169, 253.
  86. Brody, T. A., J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, 1981, Rev. Mod. Phys. 53, 385.
  87. Brouwer, P. W., 1994, unpublished.
  88. Brouwer, P. W., 1995, Phys. Rev. B 51, 16878.
  89. Brouwer, P. W., 1997, Ph.D. thesis (Leiden University, unpublished).
  90. Brouwer, P. W., and C. W. J. Beenakker, 1994, Phys. Rev. B 50, 11263.
  91. Brouwer, P. W., and C. W. J. Beenakker, 1995a, Phys. Rev. B 51, 7739.
  92. Brouwer, P. W., and C. W. J. Beenakker, 1995b, Phys. Rev. B 52, 3868.
  93. Brouwer, P. W., and C. W. J. Beenakker, 1995c, Phys. Rev. B 52, 16772.
  94. Brouwer, P. W., and C. W. J. Beenakker, 1996a, J. Math. Phys. (N.Y.) 37, 4904.
  95. Brouwer, P. W., and C. W. J. Beenakker, 1996b, Phys. Rev. B 54, 12705.
  96. Brouwer, P. W., and C. W. J. Beenakker, 1997a, Phys. Rev. B55, 4695.
  97. Brouwer, P. W., and C. W. J. Beenakker, 1997b, Chaos, Solitons and Fractals (in press).
  98. Brouwer, P. W., and M. Büttiker, 1997, Europhys. Lett. 37, 441.
  99. Brouwer, P. W., and K. M. Frahm, 1996, Phys. Rev. B 53, 1490.
  100. Bruce, N. A., and J. T. Chalker, 1996, J. Phys. A 29, 3761.
  101. Bruun, J., V. C. Hui, and C. J. Lambert, 1994, Phys. Rev. B 49, 4010.
  102. Bruus, H., C. H. Lewenkopf, and E. R. Mucciolo, 1996, Phys. Rev. B 53, 9968.
  103. Büttiker, M., 1986a, Phys. Rev. B 33, 3020.
  104. Büttiker, M., 1986b, Phys. Rev. B 57, 1761.
  105. Büttiker, M., 1988a, IBM J. Res. Dev. 32, 63.
  106. Büttiker, M., IBM J. Res. Dev. 32, 317.
  107. Büttiker, M., 1990, Phys. Rev. Lett. 65, 2901.
  108. Büttiker, M., 1992, Phys. Rev. B 46, 12485.
  109. Büttiker, M., 1993, J. Phys. Condens. Matter 5, 9361.
  110. Büttiker, M., and T. Christen, 1996, in Quantum Transport in Semiconductor Submicron Structures, edited by B. Kramer, NATO ASI Series E326 (Kluwer, Dordrecht), p. 263.
  111. Büttiker, M., A. Prêtre, and H. Thomas, 1993, Phys. Rev. Lett. 70, 4114.
  112. Calogero, F., 1969, J. Math. Phys. (N.Y.) 10, 2191.
  113. Caselle, M., 1995, Phys. Rev. Lett. 74, 2776.
  114. Chalker, J. T., and M. Bernhardt, 1993, Phys. Rev. Lett. 70, 982.
  115. Chalker, J. T., and A. Dohmen, 1995, Phys. Rev. Lett. 75, 4496.
  116. Chalker, J. T., and A. M. S. Macêdo, 1993, Phys. Rev. Lett. 71, 3693.
  117. Chan, I. H., R. M. Clarke, C. M. Marcus, K. Campman, and A. C. Gossard, 1995, Phys. Rev. Lett. 74, 3876.
  118. Chang, A. M., H. U. Baranger, L. N. Pfeiffer, and K. W. West, 1994, Phys. Rev. Lett. 73, 2111.
  119. Chang, A. M., H. U. Baranger, L. N. Pfeiffer, K. W. West, and T. Y. Chang, 1996, Phys. Rev. Lett. 76, 1695.
  120. Charlat, P., H. Courtois, Ph. Gandit, D. Mailly, A. F. Volkov, and B. Pennetier, 1996, Phys. Rev. Lett. 77, 4950.
  121. Chen, Y., M. E. H. Ismail, and K. A. Muttalib, 1992, J. Phys., Condens. Matter. 4, L417.
  122. Cho, S., and M. P. A. Fisher, 1997, Phys. Rev. B 55, 1637.
  123. Claughton, N. R., R. Raimondi, and C. J. Lambert, 1996, Phys. Rev. B 53, 9310.
  124. Cobden, D. H., and E. Kogan, 1996, Phys. Rev. B 54, 17316.
  125. Courtois, H., Ph. Gandit, D. Mailly, and B. Pannetier, 1996, Phys. Rev. Lett. 76, 130.
  126. Creutz, M., 1978, J. Math. Phys. (N.Y.) 19, 2043.
  127. Crisanti, A., G. Paladin, and A. Vulpiani, 1993, Products of Random Matrices in Statistical Physics (Springer, Berlin).
  128. Datta, S., 1995, Electronic Transport in Mesoscopic Systems (Cambridge University, Cambridge, England).
  129. Debray, P., J.-L. Pichard, J. Vicente, and P. N. Tung, 1989, Phys. Rev. Lett. 63, 2264.
  130. De Gennes, P. G., 1966, Superconductivity of Metals and Alloys (Benjamin, New York).
  131. De Jong, M. J. M., 1994, Phys. Rev. B 49, 7778.
  132. De Jong, M. J. M., and C. W. J. Beenakker, 1992, Phys. Rev. B 46, 13400.
  133. De Jong, M. J. M., and C. W. J. Beenakker, 1994, Phys. Rev. B 49, 16070.
  134. De Jong, M. J. M., and C. W. J. Beenakker, 1995, Phys. Rev. B 51, 16867.
  135. De Jong, M. J. M., and C. W. J. Beenakker, 1996, Physica A 230, 219.
  136. De Jong, M. J. M., and C. W. J. Beenakker, 1997, in Mesoscopic Electron Transport, edited by L. P. Kouwenhoven, G. Schön, and L. L. Sohn, NATO ASI Series E (Kluwer, Dordrecht), in press.
  137. Den Hartog, S. G., C. M. A. Kapteyn, B. J. van Wees, T. M. Klapwijk, W. van der Graaf, and G. Borghs, 1996, Phys. Rev. Lett. 76, 4592.
  138. De Vegvar, P. G. N., T. A. Fulton, W. H. Mallison, and R. E. Miller, 1994, Phys. Rev. Lett. 73, 1416.
  139. Dimoulas, A., J. P. Heida, B. J. van Wees, T. M. Klapwijk, W. van de Graaf, and G. Borghs, 1995, Phys. Rev. Lett. 74, 602.
  140. Dorokhov, O. N., 1982, Pis'ma Zh. Eksp. Teor. Fiz. 36, 259 [JETP Lett. 36, 318].
  141. Dorokhov, O. N., 1983, Zh. Eksp. Teor. Fiz. 85, 1040 [Sov. Phys. JETP 58, 606].
  142. Dorokhov, O. N., 1984, Solid State Commun. 51, 381.
  143. Dorokhov, O. N., 1988, Phys. Rev. B 37, 10526.
  144. Dorokhov, O. N., 1990, Zh. Eksp. Teor. Fiz. 98, 646 [Sov. Phys. JETP 71, 360].
  145. Doron, E., and U. Smilansky, 1992, Nucl. Phys. A 545, 455c.
  146. Dupuis, N., and G. Montambaux, 1991, Phys. Rev. B 43, 14390.
  147. Dyson, F. J., 1962a, J. Math. Phys. (N.Y.) 3, 140.
  148. Dyson, F. J., 1962b, J. Math. Phys. (N.Y.) 3, 157.
  149. Dyson, F. J., 1962c, J. Math. Phys. (N.Y.) 3, 1191.
  150. Dyson, F. J., 1962d, J. Math. Phys. (N.Y.) 3, 1199.
  151. Dyson, F. J., 1972, J. Math. Phys. (N.Y.) 13, 90.
  152. Dyson, F. J., and M. L. Mehta, 1963, J. Math. Phys. (N.Y.) 4, 701.
  153. Edwards, J. T., and D. J. Thouless, 1972, J. Phys. C 5, 807.
  154. Efetov, K. B., 1982, Zh. Eksp. Teor. Fiz. 83, 833 [Sov. Phys. JETP 56, 467].
  155. Efetov, K. B., 1983, Adv. Phys. 32, 53.
  156. Efetov, K. B., 1995, Phys. Rev. Lett. 74, 2299,
  157. Efetov, K. B., 1996, Supersymmetry in Disorder and Chaos (Cambridge University, Cambridge, England).
  158. Efetov, K. B., and A. I. Larkin, 1983, Zh. Eksp. Teor. Fiz. 85, 764 [Sov. Phys. JETP 58, 444].
  159. Elattari, B., V. Kagalovsky, and H. A. Weidenmüller, 1996, Nucl. Phys. A 606, 86.
  160. Endesfelder, D., 1996, Phys. Rev. B 53, 16555.
  161. Endesfelder, D., and B. Kramer, 1993, Phys. Rev. E 48, 3225.
  162. Erdös, P., and R. C. Herndon, 1982, Adv. Phys. 31, 65.
  163. Eynard, B., 1994, Los Alamos preprint archive, .
  164. Fal’ko, V. I., 1995, Phys. Rev. B 51, 5227.
  165. Fertig, H. A., and S. Das Sarma, 1989, Phys. Rev. B 40, 7410.
  166. Fisher, D. S., and P. A. Lee, 1981, Phys. Rev. B 23, 6851.
  167. Folk, J. A., S. R. Patel, S. F. Godijn, A. G. Huibers, S. M. Cronewett, C. M. Marcus, K. Campman, and A. C. Gossard, 1996, Phys. Rev. Lett. 76, 1699.
  168. Forrester, P. J., 1995, Nucl. Phys. B 435, 421.
  169. Frahm, K. M., 1995a, Phys. Rev. Lett. 74, 4706.
  170. Frahm, K. M., 1995b, Europhys. Lett. 30, 457.
  171. Frahm K. M., P. W. Brouwer, J. A. Melsen, and C. W. J. Beenakker, 1996, Phys. Rev. Lett. 76, 2981.
  172. FrahmK. M., and A.Müller-Groeling, 1996, J. Phys. A 29, 5313.
  173. Frahm, K. M., and J.-L. Pichard, 1995a, J. Phys. (France) I 5, 847.
  174. Frahm, K. M., and J.-L. Pichard, 1995b, J. Phys. (France) I 5, 877.
  175. Freidrig, H., and D. Wintgen, 1989, Phys. Rep. 183, 37.
  176. Freilikher, V., E. Kanzieper, and I. Yurkevich, 1996, Phys. Rev. E 53, 2200.
  177. Freilikher, V., M. Pustilnik, and I. Yurkevich, 1994, Phys. Rev. Lett. 73, 810.
  178. Friedman, W. A., and P. A. Mello, 1985a, Ann. Phys. (N.Y.) 161, 276.
  179. Friedman, W. A., and P. A. Mello, 1985b, J. Phys. A 18, 425.
  180. Fyodorov, Y. V., and A. D. Mirlin, 1991, Phys. Rev. Lett. 67, 2405.
  181. Fyodorov, Y. V., and A. D. Mirlin, 1994, Int. J. Mod. Phys. B 8, 3795.
  182. Gazaryan, Yu. L., 1969, Zh. Eksp. Teor. Fiz. 56, 1856 [Sov. Phys. JETP 29, 996].
  183. Gertsenshtein, M. E., and V. B. Vasil’ev, 1959, Teor. Veroyatn. Primen. 4, 424; 5, 3(E) [Theor. Probab. Appl. 4, 391; 5, 340(E)].
  184. Ghenim, L., D. L. Sivco, A. Y. Cho, and G. Hill, 1996, Phys. Rev. B 54, 11479.
  185. Goldberg, J., U. Smilansky, M. V. Berry, W. Schweizer, G. Wunner, and G. Zeller, 1991, Nonlinearity 4, 1.
  186. Golubov, A. A., and M. Yu. Kupriyanov, 1995, Pis'ma Zh. Eksp. Teor. Fiz. 61, 830 [JETP Lett. 61, 851].
  187. Golubov, A. A., F. K. Wilhelm, and A. D. Zaikin, 1997, Phys. Rev. B 55, 1123.
  188. Gopar, V. A., M. Martínez, and P. A. Mello, 1995, Phys. Rev. B 51, 16917.
  189. Gopar, V. A., M. Martínez, P. A. Mello, and H. U. Baranger, 1996, J. Phys. A 29, 881.
  190. Gopar, V. A., P. A. Mello, and M. Büttiker, 1996, Phys. Rev. Lett. 77, 3005.
  191. Gor’kov, L. P., and G. M. Eliashberg, 1965, Zh. Eksp. Teor. Fiz. 48, 1407[Sov. Phys. JETP 21, 940[.
  192. Gor’kov, L. P., A. I. Larkin, and D. E. Khmel’nitskiĭ, 1979, Pis'ma Zh. Eksp. Teor. Fiz. 30, 248 [JETP Lett. 30, 228].
  193. Gruzberg, I. A., N. Read, and S. Sachdev, 1997, Los Alamos preprint archive, .
  194. Guhr, T., 1996, Phys. Rev. Lett. 76, 2258.
  195. Gutzwiller, M. C., 1990, Chaos in Classical and Quantum Mechanics (Springer, Berlin).
  196. Haake, F., 1992, Quantum Signatures of Chaos (Springer, Berlin).
  197. Hackenbroich, G., and H. A. Weidenmüller, 1995, Phys. Rev. Lett. 74, 4118.
  198. Hamermesh, M., 1962, Group Theory and its Applications to Physical Problems (Addison-Wesley, Reading, MA).
  199. Hastings, H. B., A. D. Stone, and H. U. Baranger, 1994, Phys. Rev. B 50, 8230.
  200. Hekking, F. W. J., and Yu. V. Nazarov, 1993, Phys. Rev. Lett. 71, 1625.
  201. Hekking, F. W. J., and Yu. V. Nazarov, 1994, Phys. Rev. B 49, 6847.
  202. Holweg, P. A. M., J. A. Kokkedee, J. Caro, A. H. Verbruggen, S. Radelaar, A. G. M. Jansen, and P. Wyder, 1991, Phys. Rev. Lett. 67, 2549.
  203. Hua, L. K., 1963, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (American Mathematical Society, Providence).
  204. Huckestein, B., 1995, Rev. Mod. Phys. 67, 357.
  205. Hüffmann, A., 1990, J. Phys. A 23, 5733.
  206. Iida, S., H. A. Weidenmüller, and J. A. Zuk, 1990a, Phys. Rev. Lett. 64, 583.
  207. Iida, S., H. A. Weidenmüller, and J. A. Zuk, 1990b, Ann. Phys. (N.Y.) 200, 219.
  208. Imry, Y., 1986a, Europhys. Lett. 1, 249.
  209. Imry, Y., 1986b, in Directions in Condensed Matter Physics, edited by G. Grinstein and G. Mazenko (World Scientific, Singapore), p. 101.
  210. Imry, Y., 1995, in Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin (North-Holland, Amsterdam), p. 181.
  211. Imry, Y., 1996, Introduction to Mesoscopic Physics (Oxford University, London).
  212. Ishio, H., 1995, J. Phys. A 28, L469.
  213. Itzykson, C., and J.-B. Zuber, 1980, Quantum Field Theory (McGraw-Hill, New York).
  214. Jalabert, R. A., H. U. Baranger, and A. D. Stone, 1990, Phys. Rev. Lett. 65, 2442.
  215. Jalabert, R. A., and J.-L. Pichard, 1995, J. Phys. I 5, 287.
  216. Jalabert, R. A., J.-L. Pichard, and C. W. J. Beenakker, 1993, Europhys. Lett. 24, 1.
  217. Jalabert, R. A., J.-L. Pichard, and C. W. J. Beenakker, 1994, Europhys. Lett. 27, 255.
  218. Jalabert, R. A., A. D. Stone, and Y. Alhassid, 1992, Phys. Rev. Lett. 68, 3468.
  219. Jancovici, B., and P. J. Forrester, 1994, Phys. Rev. B 50, 14599.
  220. John, S., 1984, Phys. Rev. Lett. 53, 2169.
  221. Kadigrobov, A., A. Zagoskin, R. I. Shekhter, and M. Jonson, 1995, Phys. Rev. B 52, 8662.
  222. Kamenev, A., and Y. Gefen, 1995, Europhys. Lett. 29, 413.
  223. Kamien, R. D., H. D. Politzer, and M. B. Wise, 1988, Phys. Rev. Lett. 60, 1995.
  224. Kastalsky, A., A. W. Kleinsasser, L. H. Greene, R. Bhat, F. P. Milliken, and J. P. Harbison, 1991, Phys. Rev. Lett. 67, 3026.
  225. Keldysh, L. V., 1964, Zh. Eksp. Teor. Fiz. 47, 1515[Sov. Phys. JETP 20, 1018[.
  226. Keller, M. W., O. Millo, A. Mittal, D. E. Prober, and R. N. Sacks, 1994, Surf. Sci. 305, 501.
  227. Keller, M. W., A. Mittal, J. W. Sleight, R. G. Wheeler, D. E. Prober, R. N. Sacks, and H. Shtrikmann, 1996, Phys. Rev. B 53, 1693.
  228. Khlus, V. A., 1987, Zh. Eksp. Teor. Fiz. 93, 2179 [Sov. Phys. JETP 66, 1243].
  229. Khmel’nitskiĭ, D. E., 1984, Physica B 126, 235.
  230. Kirkman, P. D., and J. B. Pendry, 1984, J. Phys. C 17, 5707.
  231. Klapwijk, T. M., 1994, Physica B 197, 481.
  232. Kobayakawa, T. S., Y. Hatsugai, M. Kohmoto, and A. Zee, 1995, Phys. Rev. E 51, 5365.
  233. Kohler, W., and G. C. Papanicolaou, 1976, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 30, 263.
  234. Kozub, V. I., J. Caro, and P. A. M. Holweg, 1996, Physica B 218, 89.
  235. Kozub, V. I., and A. M. Rudin, 1995, Phys. Rev. B 52, 7853.
  236. Kramer, B., and A. MacKinnon, 1993, Rep. Prog. Phys. 56, 1469.
  237. Krieger, T. J., 1965, Ann. Phys. (N.Y.) 42, 375.
  238. Kulik, I. O., and A. N. Omel’yanchuk, 1984, Fiz. Nizk. Temp. 10, 305 [Sov. J. Low Temp. Phys. 10, 158].
  239. Kulik, I. O., and R. I. Shekhter, 1975, Zh. Eksp. Teor. Fiz. 68, 623 [Sov. Phys. JETP 41, 308].
  240. Kumar, N., 1985, Phys. Rev. B 31, 5513.
  241. Lagendijk, A., and B. A. van Tiggelen, 1996, Phys. Rep. 270, 143.
  242. Lambert, C. J., 1991, J. Phys., Condens. Matter. 3, 6579.
  243. Lambert, C. J., 1993, J. Phys., Condens. Matter. 5, 707.
  244. Lambert, C. J., V. C. Hui, and S. J. Robinson, 1993, J. Phys., Condens. Matter. 5, 4187.
  245. Landauer, R., 1957, IBM J. Res. Dev. 1, 223.
  246. Landauer, R., 1970, Philos. Mag. 21, 863.
  247. Landauer, R., 1987, Z. Phys. B 68, 217.
  248. Larkin, A. I., and Yu. V. Ovchinnikov, 1975, Zh. Eksp. Teor. Fiz. 68, 1915 [Sov. Phys. JETP 41, 960].
  249. Larkin, A. I., and Yu. V. Ovchinnikov, 1977, Zh. Eksp. Teor. Fiz. 73, 299 [Sov. Phys. JETP 46, 155].
  250. Lee, P. A., and T. V. Ramakrishnan, 1985, Rev. Mod. Phys. 57, 287.
  251. Lee, P. A., and A. D. Stone, 1985, Phys. Rev. Lett. 55, 1622.
  252. Lenssen, K.-M. H., P. C. A. Jeekel, C. J. P. M. Harmans, J. E. Mooij, M. R. Leys, J. H. Wolter, and M. C. Holland, 1994, in Coulomb and Interference Effects in Small Electronic Structures, edited by D. C. Glattli, M. Sanquer, and J. Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, France), p. 63.
  253. Lenz, G., and F. Haake, 1990, Phys. Rev. Lett. 65, 2325.
  254. Leo, J., and A. H. MacDonald, 1990, Phys. Rev. Lett. 64, 817.
  255. Lerner, I. V., and Y. Imry, 1995, Europhys. Lett. 29, 49.
  256. Lerner, I. V., and M. E. Raikh, 1992, Phys. Rev. B 45, 14036.
  257. Lesovik, G. B., 1989, Pis'ma Zh. Eksp. Teor. Fiz. 49, 513 [JETP Lett. 49, 592].
  258. Lesovik, G. B., A. L. Fauchère, and G. Blatter, 1997, Phys. Rev. B 55, 3146.
  259. Lewenkopf, C. H., and H. A. Weidenmüller, 1991, Ann. Phys. (N.Y.) 212, 53.
  260. Liefrink, F., J. I. Dijkhuis, M. J. M. de Jong, L. W. Molenkamp, and H. van Houten, 1994, Phys. Rev. B 49, 14066.
  261. Likharev, K. K., 1979, Rev. Mod. Phys. 51, 101.
  262. Macêdo, A. M. S., 1994a, Phys. Rev. B 49, 1858.
  263. Macédo, A. M. S., 1994b, Phys. Rev. B 49, 16841.
  264. Macédo, A. M. S., 1996, Phys. Rev. B 53, 8411.
  265. Macédo, A. M. S., and J. T. Chalker, 1992, Phys. Rev. B 46, 14985.
  266. Macédo, A. M. S., and J. T. Chalker, 1994, Phys. Rev. B 49, 4695.
  267. Magnée, P. H. C., N. van der Post, P. H. M. Kooistra, B. J. van Wees, and T. M. Klapwijk, 1994, Phys. Rev. B 50, 4594.
  268. Mahaux, C., and H. A. Weidenmüller, 1969, Shell-Model Approach to Nuclear Reactions (North-Holland, Amsterdam).
  269. Mailly, D., and M. Sanquer, 1992, J. Phys. (France) I 2, 357.
  270. Makeenko, Yu., 1991, Mod. Phys. Lett. A 6, 1901.
  271. Mani, R. G., L. Ghenim, and T. N. Theis, 1992, Phys. Rev. B 45, 12098.
  272. Marcus, C. M., 1996, unpublished.
  273. Marcus, C. M., A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, 1992, Phys. Rev. Lett. 69, 506.
  274. Marcus, C. M., R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, 1993, Phys. Rev. B 48, 2460.
  275. Marmorkos, I. K., C. W. J. Beenakker, and R. A. Jalabert, 1993, Phys. Rev. B 48, 2811.
  276. Martin, Th., 1994, in Coulomb and Interference Effects in Small Electronic Structures, edited by D. C. Glattli, M. Sanquer, and J. Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, France), p. 405.
  277. Martin, Th., 1996, Phys. Lett. A 220, 137.
  278. Martin, Th., and R. Landauer, 1992, Phys. Rev. B 45, 1742.
  279. Martin, Th., G. Montambaux, and J. Trân Thanh Vân, Eds. 1996, Correlated Fermions and Transport in Mesoscopic Systems (Editions Frontières, Gif-sur-Yvette, France).
  280. Maslov, D. L., C. Barnes, and G. Kirczenow, 1993a, Phys. Rev. Lett. 70, 1984.
  281. Maslov, D. L., C. Barnes, and G. Kirczenow, 1993b, Phys. Rev. B 48, 2543.
  282. Maxwell, J. C., 1891, A Treatise on Electricity and Magnetism (Dover, New York).
  283. McCann, E., and I. V. Lerner, 1996, J. Phys., Condens. Matter. 8, 6719.
  284. Mehta, M. L., 1991, Random Matrices (Academic, New York).
  285. Mehta, M. L., and A. Pandey, 1983, J. Phys. A 16, L601.
  286. Meir, Y., and O. Entin-Wohlman, 1993, Phys. Rev. Lett. 70, 1988.
  287. Meir, Y., N. S. Wingreen, O. Entin-Wohlman, and B. L. Altshuler 1991, Phys. Rev. Lett. 66, 1517.
  288. Meir, Y., N. S. Wingreen, and P. A. Lee, 1991, Phys. Rev. Lett. 66, 3048.
  289. Meirav, U., and E. B. Foxman, 1995, Semicond. Sci. Technol. 10, 255.
  290. Mello, P. A., 1986, J. Math. Phys. (N.Y.) 27, 2876.
  291. Mello, P. A., 1988, Phys. Rev. Lett. 60, 1089.
  292. Mello, P. A., 1990, J. Phys. A 23, 4061.
  293. Mello, P. A., 1995, in Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin (North-Holland, Amsterdam), p. 435.
  294. Mello, P. A., E. Akkermans, and B. Shapiro, 1988, Phys. Rev. Lett. 61, 459.
  295. Mello, P. A., P. Pereyra, and N. Kumar, 1988, Ann. Phys. (N.Y.) 181, 290.
  296. Mello, P. A., P. Pereyra, and T. H. Seligman, 1985, Ann. Phys. (N.Y.) 161, 254.
  297. Mello, P. A., and J.-L. Pichard, 1989, Phys. Rev. B 40, 5276.
  298. Mello, P. A., and J.-L. Pichard, 1991, J. Phys. (France) I 1, 493.
  299. Mello, P. A., and B. Shapiro, 1988, Phys. Rev. B 37, 5860.
  300. Mello, P. A., and A. D. Stone, 1991, Phys. Rev. B 44, 3559.
  301. Mello, P. A., and S. Tomsovic, 1991, Phys. Rev. Lett. 67, 342.
  302. Mello, P. A., and S. Tomsovic, 1992, Phys. Rev. B 46, 15963.
  303. Mel’nikov, V. I., 1981, Fiz. Tverd. Tela (Leningrad) 23, 782 [Sov. Phys. Solid State 23, 444].
  304. Melsen, J. A., and C. W. J. Beenakker, 1994, Physica B 203, 219.
  305. Melsen, J. A., and C. W. J. Beenakker, 1995, Phys. Rev. B 51, 14483.
  306. Melsen, J. A., P. W. Brouwer, K. M. Frahm, and C. W. J. Beenakker, 1996, Europhys. Lett. 35, 7.
  307. Mikhlin, S. G., 1964, Integral Equations (Pergamon, New York).
  308. Millo, O., S. J. Klepper, M. W. Keller, D. E. Prober, S. Xiong, A. D. Stone, and R. N. Sacks, 1990, Phys. Rev. Lett. 65, 1494.
  309. Mirlin, A. D., 1994, Phys. Rev. Lett. 72, 3437.
  310. Mirlin, A. D., A. Müller-Groeling, and M. R. Zirnbauer, 1994, Ann. Phys. (N.Y.) 236, 325.
  311. Morita, Y., Y. Hatsugai, and M. Kohmoto, 1995, Phys. Rev. B 52, 4716.
  312. Mucciolo, E. R., V. N. Prigodin, and B. L. Altshuler, 1995, Phys. Rev. B 51, 1714.
  313. Muttalib, K. A., 1990, Phys. Rev. Lett. 65, 745.
  314. Muttalib, K. A., 1995, J. Phys. A 28, L159.
  315. Muttalib, K. A., Y. Chen, M. E. H. Ismail, and V. N. Nicopoulos, 1993, Phys. Rev. Lett. 71, 471.
  316. Muttalib, K. A., J.-L. Pichard, and A. D. Stone, 1987, Phys. Rev. Lett. 59, 2475.
  317. Muzykantskiĭ, B. A., and D. E. Khmel’nitskiĭ, 1994, Physica B 203, 233.
  318. Muzykantskiĭ, B. A., and D. E. Khmel’nitskiĭ, 1995, Pis’ma Zh. Eksp. Teor. Fiz. 62, 68 [JETP Lett. 62, 76].
  319. Nagaev, K. E., 1992, Phys. Lett. A 169, 103.
  320. Nagaev, K. E., 1995, Phys. Rev. B 52, 4740.
  321. Nazarov, Yu. V., 1994a, Phys. Rev. Lett. 73, 134.
  322. Nazarov, Yu. V., 1994b, Phys. Rev. Lett. 73, 1420.
  323. Nazarov, Yu. V., 1995a, in Quantum Dynamics of Submicron Structures, edited by H. A. Cerdeira, B. Kramer, and G. Schön, NATO ASI Series E291 (Kluwer, Dordrecht), p. 687.
  324. Nazarov, Yu. V., 1995b, Phys. Rev. B 52, 4720.
  325. Nazarov, Yu. V., 1996, Phys. Rev. Lett. 76, 2129.
  326. Nazarov, Yu. V., and T. H. Stoof, 1996, Phys. Rev. Lett. 76, 823.
  327. Ng, T. K., and P. A. Lee, 1988, Phys. Rev. Lett. 61, 1768.
  328. Nguyen, C., H. Kroemer, and E. L. Hu, 1992, Phys. Rev. Lett. 69, 2847.
  329. Nguyen, V. I., B. Z. Spivak, and B. I. Shklovskiĭ, 1985, Pis'ma Zh. Eksp. Teor. Fiz. 41, 35 [JETP Lett. 41, 42].
  330. Nieuwenhuizen, Th. M., and J. M. Luck, 1993, Phys. Rev. E 48, 569.
  331. Nishioka, H., and H. A. Weidenmüller, 1985, Phys. Lett. B 157, 101.
  332. Oseledec, V. I., 1968, Trans. Moscow Math. Soc. 19, 197.
  333. Paasschens, J. C. J., T. Sh. Misirpashaev, and C. W. J. Beenakker, 1996, Phys. Rev. B 54, 11887.
  334. Pandey, A., and M. L. Mehta, 1983, Commun. Math. Phys. 87, 449.
  335. Pandey, A., and P. Shukla, 1991, J. Phys. A 24, 3907.
  336. Papanicolaou, G. C., 1971, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 21, 13.
  337. Pastur, L. A., 1992, Lett. Math. Phys. 25, 259.
  338. Pendry, J. B., 1994, Adv. Phys. 43, 461.
  339. Pendry, J. B., A. MacKinnon, and P. J. Roberts, 1992, Proc. R. Soc. London 437, 67.
  340. Pereyra, P., and P. A. Mello, 1983, J. Phys. A 16, 237.
  341. Petrashov, V. T., V. N. Antonov, P. Delsing, and T. Claeson, 1995, Phys. Rev. Lett. 74, 5268.
  342. Pichard, J.-L., 1984, Ph.D. Thesis (University of Paris at Orsay).
  343. Pichard, J.-L., 1991, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer, NATO ASI Series B254 (Plenum, New York), p. 369.
  344. Pichard, J.-L., and G. André, 1986, Europhys. Lett. 2, 477.
  345. Pichard, J.-L., M. Sanquer, K. Slevin, and Ph. Debray, 1990, Phys. Rev. Lett. 65, 1812.
  346. Pichard, J.-L., and G. Sarma, 1981, J. Phys. C 14, L127.
  347. Pichard, J.-L., N. Zanon, Y. Imry, and A. D. Stone, 1990, J. Phys. (France) 51, 587.
  348. Pluhař, Z., H. A. Weidenmüller, J. A. Zuk, and C. H. Lewenkopf, 1994, Phys. Rev. Lett. 73, 2115.
  349. Pluhař, Z., H. A. Weidenmüller, J. A. Zuk, C. H. Lewenkopf, and F. J. Wegner, 1995, Ann. Phys. (N.Y.) 243, 1.
  350. Poilblanc, D., T. Ziman, J. Bellissard, F. Mila, and G. Montambaux, 1993, Europhys. Lett. 22, 537.
  351. Poirier, W., D. Mailly, and M. Sanquer, 1996, in Correlated Fermions and Transport in Mesoscopic Systems, edited by Th. Martin, G. Montambaux, and J. Trân Thanh Vân (Editions Frontières, Gif-sur-Yvette, France).
  352. Politzer, H. D., 1989, Phys. Rev. B 40, 11917.
  353. Porter, C. E., 1965, Statistical Theories of Spectra: Fluctuations (Academic, New York).
  354. Pothier, H., S. Guéron, D. Esteve, and M. H. Devoret, 1994, Phys. Rev. Lett. 73, 2488.
  355. Pradhan, P., and N. Kumar, 1994, Phys. Rev. B 50, 9644.
  356. Prange, R. E., and S. M. Girvin, Eds., 1990, The Quantum Hall Effect (Springer, New York).
  357. Prigodin, V. N., B. L. Altshuler, K. B. Efetov, and S. Iida, 1994, Phys. Rev. Lett. 72, 546.
  358. Prigodin, V. N., K. B. Efetov, and S. Iida, 1993, Phys. Rev. Lett. 71, 1230.
  359. Prigodin, V. N., K. B. Efetov, and S. Iida, 1995, Phys. Rev. B 51, 17223.
  360. Raikh, M. E., and I. M. Ruzin, 1991, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam), p. 315.
  361. Rammal, R., and B. Doucot, 1987, J. Phys. (France) 48, 509.
  362. Rau, J., 1995, Phys. Rev. B 51, 7734.
  363. Rejaei, B., 1996, Phys. Rev. B 53, 13235.
  364. Samuel, S., 1980, J. Math. Phys. (N.Y.) 21, 2695.
  365. Sharvin, Yu. V., 1965, Zh. Eksp. Teor. Fiz. 48, 984[Sov. Phys. JETP 21, 655[.
  366. Shekhter, R. I., 1972, Zh. Eksp. Teor. Fiz. 63, 1410 [Sov. Phys. JETP 36, 747 (1973)].
  367. Shelankov, A. L., 1980, Pis'ma Zh. Eksp. Teor. Fiz. 32, 122 [JETP Lett. 32, 111].
  368. Shelankov, A. L., 1984, Fiz. Tverd. Tela (Leningrad) 26, 1615 [Sov. Phys. Solid State 26, 981].
  369. Shepelyansky, D. L., 1994, Phys. Rev. Lett. 73, 2607.
  370. Shklovskiĭ, B. I., and B. Z. Spivak, 1990, in Hopping Conduction in Semiconductors, edited by M. Pollak and B. I. Shklovskiĭ (North-Holland, Amsterdam).
  371. Simons, B. D., and B. L. Altshuler, 1993, Phys. Rev. Lett. 70, 4063.
  372. Sivan, U., Y. Imry, and A. G. Aronov, 1994, Europhys. Lett. 28, 115.
  373. Sivan, U., F. P. Milliken, K. Milkove, S. Rishton, Y. Lee, J. M. Hong, V. Boegli, D. Kern, and M. DeFranza, 1994, Europhys. Lett. 25, 605.
  374. Slevin, K., and T. Nagao, 1993, Phys. Rev. Lett. 70, 635.
  375. Slevin, K., and T. Nagao, 1994, Phys. Rev. B 50, 2380.
  376. Slevin, K., J.-L. Pichard, and P. A. Mello, 1991, Europhys. Lett. 16, 649.
  377. Slevin, K., J.-L. Pichard, and P. A. Mello, 1996, J. Phys. (France) I 6, 529.
  378. Slevin, K., J.-L. Pichard, and K. A. Kuttalib, 1993, J. Phys. (France) I 3, 1387.
  379. Smilansky, U., 1990, in Chaos and Quantum Physics, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (North-Holland, Amsterdam), p. 371.
  380. Spivak, B. Z., and D. E. Khmel’nitskiĭ, 1982, Pis'ma Zh. Eksp. Teor. Fiz. 35, 334 [JETP Lett. 35, 412].
  381. Steinbach, A. H., J. M. Martinis, and M. H. Devoret, 1995, Bull. Am. Math. Soc. 40, 400.
  382. Steinbach, A. H., J. M. Martinis, and M. H. Devoret, 1996, Phys. Rev. Lett. 76, 3806.
  383. Stone, A. D., P. A. Mello, K. A. Muttalib, and J.-L. Pichard, 1991, in Mesoscopic Phenomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (North-Holland, Amsterdam), p. 369.
  384. Stone, A. D., and A. Szafer, 1988, IBM J. Res. Dev. 32, 384.
  385. Stoof, T.H., and Yu. V. Nazarov, 1996a, Phys. Rev. B 53, 1050.
  386. Stoof, T.H., and Yu. V. Nazarov, 1996b, Phys. Rev. B 54, 772.
  387. Sutherland, B., 1971, J. Math. Phys. (N.Y.) 12, 246.
  388. Sutherland, B., 1972, Phys. Rev. A 5, 1372.
  389. Szafer, A., and B. L. Altshuler, 1993, Phys. Rev. Lett. 70, 587.
  390. Szafer, A., and A. D. Stone, 1989, Phys. Rev. Lett. 62, 300.
  391. Takane, Y., and H. Ebisawa, 1991, J. Phys. Soc. Jpn. 60, 3130.
  392. Takane, Y., and H. Ebisawa, 1992a, J. Phys. Soc. Jpn. 61, 1685.
  393. Takane, Y., and H. Ebisawa, 1992b, J. Phys. Soc. Jpn. 61, 2858.
  394. Takane, Y., and H. Ebisawa, 1993, J. Phys. Soc. Jpn. 62, 1844.
  395. Takane, Y., and H. Otani, 1994, J. Phys. Soc. Jpn. 63, 3361.
  396. Takayanagi, H., E. Toyoda, and T. Akazaki, 1996, unpublished.
  397. Tartakovski, A. V., 1995, Phys. Rev. B 52, 2704.
  398. Thouless, D. J., 1977, Phys. Rev. Lett. 39, 1167.
  399. Van Albada, M. P., B. A. van Tiggelen, A. Lagendijk, and A. Tip, 1991, Phys. Rev. Lett. 66, 3132.
  400. Van Houten, H., C. W. J. Beenakker, and A. A. M. Staring, 1992, in Single Charge Tunneling, edited by H. Grabert and M. H. Devoret (Plenum, New York), p. 167.
  401. Van Kampen, N. G., 1981, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam).
  402. Van Langen, S. A., P. W. Brouwer, and C. W. J. Beenakker, 1996, Phys. Rev. E 53, 1344.
  403. Van Son, P. C., H. van Kempen, and P. Wyder, 1987, Phys. Rev. Lett. 59, 2226.
  404. Van Son, P. C., H. van Kempen, and P. Wyder, 1988, J. Phys. F 18, 2211.
  405. Van Wees, B. J., P. de Vries, P. Magnée, and T. M. Klapwijk, 1992, Phys. Rev. Lett. 69, 510.
  406. Van Wees, B. J., and H. Takayanagi, 1997, in Mesoscopic Electron Transport, edited by L. P. Konwenhoven, G. Schön, and L. L. Sohn, NATO ASI Series E (Kluwer, Dordrecht), in press.
  407. Verbaarschot, J. J. M., H. A. Weidenmüller, and M. R. Zirnbauer, 1985, Phys. Rep. 129, 367.
  408. Volkov, A. F., 1994, Phys. Lett. A 187, 404.
  409. Volkov, A. F., N. Allsopp, and C. J. Lambert, 1996, J. Phys., Condens. Matter. 8, L45.
  410. Volkov, A. F., and A. V. Zaǐtsev, 1996, Phys. Rev. B 53, 9267.
  411. Volkov, A. F., A. V. Zaǐtsev, and T. M. Klapwijk, 1993, Physica C 210, 21.
  412. Vollhardt, D., and P. Wölfle, 1992, in Electronic Phase Transitions, edited by W. Hanke and Yu. V. Kopaev (North-Holland, Amsterdam), p. 1.
  413. Wang, Z., B. Jovanović, and D.-H. Lee, 1996, Phys. Rev. Lett. 77, 4426.
  414. Washburn, S., and R. A. Webb, 1986, Adv. Phys. 35, 375.
  415. Wegner, F., 1979, Z. Phys. B 35, 207.
  416. Weidenmüller, H. A., 1990, Physica A 167, 28.
  417. Westervelt, R. M., 1996, in Nano-Science and Technology, edited by G. Timp (American Institute of Physics, New York), in press.
  418. Wigner, E. P., 1957, in Proceedings of the Canadian Mathematical Congress (University of Toronto, Toronto), p. 174; reprinted in Porter (1965), p. 188.
  419. Wigner, E. P., 1967, SIAM (Soc. Ind. Appl. Math.) Rev. 9, 1.
  420. Xiong, P., G. Xiao, and R. B. Laibowitz, 1993, Phys. Rev. Lett. 71, 1907.
  421. Yang, X., H. Ishio, and J. Burgdörfer, 1995, Phys. Rev. B 52, 8219.
  422. Yip, S., 1995, Phys. Rev. B 52, 15504.
  423. Yurke, B., and G. P. Kochanski, 1990, Phys. Rev. B 41, 8184.
  424. Zaĭtsev, A. V., 1980, Zh. Eksp. Teor. Fiz. 78, 221; 79, 2016(E) [Sov. Phys. JETP 51, 111; 52, 1018(E)].
  425. Zaĭtsev, A. V., 1984, Zh. Eksp. Teor. Fiz. 86, 1742 [Sov. Phys. JETP 59, 1015].
  426. Zaĭtsev, A. V., 1994, Phys. Lett. A 194, 315.
  427. Zanon, N., and J.-L. Pichard, 1988, J. Phys. (France) 49, 907.
  428. Zhang, Z. Q., 1995, Phys. Rev. B 52, 7960.
  429. Zhou, F., and B. Spivak, 1996, Los Alamos preprint archive, .
  430. Zhou, F., B. Spivak, and A. Zyuzin, 1995, Phys. Rev. B 52, 4467.
  431. Zirnbauer, M. R., 1992, Phys. Rev. Lett. 69, 1584.
  432. Zirnbauer, M. R., 1993, Nucl. Phys. A 560, 95.

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