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Stick-breaking model for variable-range hopping

Wilkinson, M.; Mehlig, B. and Bezuglyy, V. (2008). Stick-breaking model for variable-range hopping. Philosophical Magazine Letters, 88(5) pp. 327–344.

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We consider the optimal conduction path of the one-dimensional variable-range hopping problem. We describe a hierarchical procedure for constructing the path which is in excellent agreement with numerical results obtained from a percolation approach. The advantage of the hierarchical construction is that it is easier to analyse. We show that the distribution of hopping lengths is well-approximated by a model for the repeated breaking of a stick at its weakest point, until the fragments are too strong to be broken.

Item Type: Journal Article
Copyright Holders: 2010 Taylor and Francis
ISSN: 0950-0839
Keywords: disordered materials; electrical transport; hopping conduction; localised states
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 25386
Depositing User: Michael Wilkinson
Date Deposited: 11 Dec 2010 16:56
Last Modified: 04 Jan 2011 15:32
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