Stick-Breaking Model for Variable-Range Hopping
Disordered Systems and Neural Networks
2009-11-13 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0709.3317,
title = {Stick-Breaking Model for Variable-Range Hopping},
author = {M. Wilkinson and B. Mehlig and V. Bezuglyy},
journal= {arXiv preprint arXiv:0709.3317},
year = {2009}
}
Comments
4 pages, 3 figures