Stick-Breaking Model for Variable-Range Hopping

Details Stick-Breaking Model for Variable-Range Hopping Stick-Breaking Model for Variable-Range Hopping

2007-09-20

arxiv.org/abs/0709.3317v1

Phil. Mag. Lett. 88, 327 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1080/09500830801971462

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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