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Tunneling resistance of a one dimensional random lattice Carvalho, Isabel Cristina Dos Santos
Abstract
The resistivity of a one-dimensional lattice consisting of randomly distributed conductivity and insulating sites is considered. Tunneling resistance of the form R[sub o] i e[sup bi] is assumed for a cluster of i adjacent insulating sites. Three different ensembles are considered and compared. In the first ensemble the number of insulating "atoms" is fixed and distributed in a linear chain; in the second one there exists a fixed probability p of having an insulator "atom" occupying a site in a linear chain, and finally the third one consists of a line bent into a circle and the probability p is considered. It is observed that in the thermodynamic limit, the average ensemble resistance per site diverges at the critical filling fraction p[sub c] = e[sup –b], while the variance of the resistance diverges at the lower filling fraction p[sub c1] = p[sup 2/c] . Computer simulations of large but finite systems, however, exhibit a much weaker divergence of the resistance per site at p[sub c] and no divergence of the variance at P[sub c1].
Item Metadata
Title |
Tunneling resistance of a one dimensional random lattice
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1984
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Description |
The resistivity of a one-dimensional lattice consisting of randomly distributed conductivity and insulating sites is considered. Tunneling resistance of the form R[sub o] i e[sup bi] is assumed for a cluster of i adjacent insulating sites. Three different ensembles are considered and compared. In the first ensemble the number of insulating "atoms" is fixed and distributed in a linear chain; in the second one there exists a fixed probability p of having an insulator "atom" occupying a site in a linear chain, and finally the third one consists of a line bent into a circle and the probability p is considered. It is observed that in the thermodynamic limit, the average ensemble resistance per site diverges at the critical filling fraction p[sub c] = e[sup –b], while the variance of the resistance
diverges at the lower filling fraction p[sub c1] = p[sup 2/c] . Computer simulations of
large but finite systems, however, exhibit a much weaker divergence of the resistance per site at p[sub c] and no divergence of the variance at P[sub c1].
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Genre | |
Type | |
Language |
eng
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Date Available |
2010-05-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0096045
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.