ISSN:
1572-9613
Keywords:
Tunneling
;
resistivity
;
Petersburg problem
;
random lattice
;
fluctuations
;
critical filling
;
mean and most probable values
;
divergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The resistivity of a one-dimensional lattice consisting of randomly distributed conducting and insulating sites is considered. Tunneling resistance of the form ρ0 ne bn is assumed for a cluster ofn adjacent insulating sites. In the thermodynamic limit, the mean resistance per site diverges at the critical filling fractionp c =e−b, while the mean square resistivity fluctuations diverge at the lower filling fraction $$p_{c_2 } $$ =p c 2 . Computer simulations of large but finite systems, however, show only a very weak divergence of resistivity atp c and no divergence of the fluctuations at $$p_{c_2 } $$ . For finite lattices, calculation of the resistivity at the critical filling is shown to be simply related to the Petersburg problem. Analytic expressions for the resistivity and resistivity fluctuations are obtained in agreement with the results of computer simulations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01017369
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