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.



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.

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