Abstract
Electrical conductance is typically calculated by approaches which view the electrical field as a causative source and the motion of carriers as a response. An alternative viewpoint, which starts from the flux of carriers maintained at the edges of a sample, and then calculates how charges build up and fields develop, has gained acceptance in the treatment of disordered systems, the solid state Aharanov-Bohm effect, and universal fluctuations. We analyze some of the less appreciated concomitants of this viewpoint, emphasizing both the generality and limitations of the viewpoint. Particular emphasis is given to the Residual Resistivity Dipole; localized scatterers in metallic conductivity are accompanied by highly localized transport fields. Closed Hamiltonian systems, e.g. a metallic ring with elastic scattering and driven by a time-dependent magnetic flux, are conservative. They cannot exhibit dissipation, under our conventionally accepted forms of physics. It is suggested that the limited precision available,in principle, in calculating the behavior of physical systems limits our ability to retrieve energy from supposedly conservative systems. This can be regarded as the ultimate source of dissipative processes.
Similar content being viewed by others
References
Kohn, W., Luttinger, J.M.: Phys. Rev.108, 590 (1957); ibid.109, 1892 (1958)
Kubo, R.: Science233, 330 (1986)
Landauer, R.: IBM J. Res. Dev.1, 223 (1957)
Landauer, R.: Philos. Mag.21, 863 (1970)
Landauer, R.: Z. Phys. B—Condensed Matter and Quanta21, 247 (1975)
Landauer, R.: In: Localization interaction and transport phenomena. Kramer, B., Bergmann, G., Bruynseraede, Y. (eds.), p. 38. Berlin, Heidelberg, New York: Springer 1985
Landauer, R.: Personal comments on the stone age of localization (unpublished) June 1983
Anderson, P.W., Thouless, D.J., Abrahams, E., Fisher, D.: Phys. Rev. B22, 3519 (1980)
Frensley, W.R.: Phys. Rev. Lett.57, 2853 (1986)
Washburn, S., Webb, R.A.: Adv. Phys.35, 375 (1986)
Landauer, R., Büttiker, M.: Diffusive traversal time: effective area in magnetically induced interference. Phys. Rev. B (in press)
Lee, P.A., Stone, A.D., Fukuyama, H.: Phys. Rev. B35, 1039 (1987)
Lee, P.A.: In: Statphys. 16, Thermodynamics and Statistical Mechanics. Stanley, H.E. (ed.), p. 169, Amsterdam: North-Holland 1986
Imry, Y.: Europhys. Lett.1, 249 (1986)
Al'tshuler, B.L.: JETP Lett.41, 648 (1985)
Feng, S., Lee, P.A., Stone, A.D.: Phys. Rev. Lett.56, 1960 (1986); ibid. Erratum56, 2772 (1986)
Büttiker, M.: Phys. Rev. B35, 4123 (1987)
Payne, M.C., Levi, A.F.J., Phillips, W.A., Inkson, J.C., Adkins, C.J.: J. Phys. C17, 1643 (1984)
Al'tshuler, B.L.: JETP Lett.41, 648 (1985)
Lee, P.A., Ramakrishnan, T.V.: Rev. Mod. Phys.57, 287 (1985)
Hu P.: Phys. Rev. B35, 4078 (1987); Landauer, R.: In: Nonlinearity in condensed matter. Bishop, A.R., Campbell, D.K., Trullinger, S.E., Kumar, P. (eds.), p. 2. Berlin, Heidelberg, New York: Springer 1987; see also Ref. 39
Das, A.K., Peierls, R.E.: Phys. C8, 3348 (1975); Turban, L., Nozières, P., Gerl, M.: J. Phys. (Paris)37, 159 (1976); Sham, L.: Phys. Rev. B12, 3142 (1975)
Sorbello, R.S.: In: Macroscopic properties of disordered media. Burridge, R., Childress, S., Papanicolaou, G. (eds.), p. 251. Berlin, Heidelberg, New York: Springer 1982
Sorbello, R.S.: Phys. Rev. B31, 798 (1985)
Verbruggen, A.H., Griessen, R., Groot, D.G. de: J. Phys. F16, 557 (1986)
Verbruggen, A.H., Griessen, R., Rector, J.H.: Phys. Rev. Lett.18, 1625 (1984)
Verbruggen, A.H.: Electromigration and proton-Hall effect in methalhydrides. Ph.D. Thesis, Amsterdam: Rodopi, 1985. Verbruggen's experimental thesis presents the best available broad overview of the theory
Gupta, R.P.: Solid State Commun.59, 219 (1986)
Landauer, R.: In: Electrical transport and optical properties of inhomogeneous Media. Garland, J.C., Tanner, D.B. (eds.), Sect. 11, p. 32. New York: AIP 1978
Büttiker, M., Imry, Y., Landauer, R.: Phys. Lett.96A, 365 (1983)
Büttiker, M., Imry, Y., Landauer, R., Pinhas, S.: Phys. Rev. B31, 6207 (1985)
Gefen, Y., Imry, Y., Azbel, M.Ya.: Phys. Rev. Lett.52, 129 (1984)
Schwarzschild, B.: Physics Today39, 17 (Jan. 1986)
Sommerfeld, A., Bethe, H.: In: Handbuch der Physik, 2nd ed., Vol. 24, p. 446. Berlin: Springer 1933
Erdös, P., Herdon, R.C.: Adv. Phys.31, 65 (1982)
Landauer, R., Woo, J.W.F.: Phys. Rev. B5, 1189 (1972); see also Sect. 5 of [5]
Engquist, H.-L., Anderson, P.W.: Phys. Rev. B24, 1151 (1981)
see also Entin-Wohlman, O., Hartzstein, C., Imry, Y.: Phys. Rev. B34, 921 (1986)
Büttiker, M.B.: Phys. Rev. Lett.57, 1761 (1986)
Benoit, A., Umbach, C.P., Laibowitz, R.B., Webb, R.A.: Phys. Rev. Lett.58, 2343 (1987)
Azbel, M.Ya.: Solid State Commun.45, 527 (1983)
Azbel, M.Ya., Hartstein, A., DiVincenzo, D.P.: Phys. Rev. Lett.52, 1641 (1984)
Tsu, R., Esaki, L.: Appl. Phys. Lett.22, 562 (1973)
Büttiker, M.: Phys. Rev. B33, 3020 (1986); See also Büttiker, M.: IBM J. Res. Dev. (in press)
Enz, C.P.: Phys. Lett. A119, 432 (1987)
Uwaha, M., Nozières, P.: J. Phys.46, 109 (1985)
Castaing, B., Nozières, P.: J. Phys.41, 701 (1980)
Eränen, S., Sinkkonen, J.: Phys. Rev. B35, 2222 (1987)
Büttiker, M.: (unpublished)
Kumar, N., Jayannavar, A.M.: Phys. Rev. B32, 3345 (1985)
Imry, Y.: In: Directions in condensed matter physics, memorial volume in honor of Shangkeng Ma, S-k., Grinstein, G., Mazenko, G. (eds.), p. 101. Singapore: World Scientific, 1986
Sivan, U., Imry, Y.: Phys. Rev. B33, 551 (1986)
Jansen, A.G.M., Wyder, P., van Kempen, H.: Europhys. News18, 21 (1987)
Sharvin, Yu.V.: Sov. Phys.-JETP21, 655 (1965)
Crandall, I.B.: Theory of vibrating systems and sound. Sect. 44, Princeton, van Nostrand 1954
Shapiro, B.: Phys. Rev. Lett.50, 747 (1983)
Hänggi, P., Thomas, H.: Phys. Rep.88, 207 (1982)
Gardiner, C.W.: Handbook of stochastic methods. 2nd Edn. Berlin, Heidelberg, New York: Springer 1985
van Kampen, N.G.: Stochastic processes in physics and chemistry. Amsterdam: North-Holland 1981
Carini, J.P., Muttalib, K.A., Nagel, S.R.: Phys. Rev. Lett.53, 102 (1984)
Landauer, R.: Phys. Rev. B33, 6497 (1986)
Landauer, R., Büttiker, M.: Phys. Rev. Lett.54, 2049 (1985)
Büttiker, M.: Phys. Scr.I 14, 82 (1986)
Landauer, R.: Resistance in metallic rings. Phys. Rev. Lett.58, 2150 (1987)
Lenstra, D., Haeringen, W. van: Phys. Rev. Lett.57, 1623 (1986)
Caldeira, A.O., Leggett, A.J.: Ann. Phys. (NY)149, 374 (1983)
Schmid, A.: Ann. Phys. (NY)170, 333 (1986)
Landauer, R.: IEEE Spectrum4, 105 (1967)
Landauer, R.: Phys. Scr.35, 88 (1987)
Landauer, R.: Found. Phys.16, 551 (1986)
Landauer, R.: In: Der Informationsbegriff in Technik und Wissenschaft. Folberth, O.G., Hackl, C. (Hrsg.), p. 139. München: Oldenbourg 1986
Landauer, R.: Ber. Bunsenges.80, 1048 (1986)
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Harry Thomas on the occasion of his 60th birthday
Rights and permissions
About this article
Cite this article
Landauer, R. Electrical transport in open and closed systems. Z. Physik B - Condensed Matter 68, 217–228 (1987). https://doi.org/10.1007/BF01304229
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01304229