Year: 2008
Type: article
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.
Source: Philosophical Magazine Letters
Authors: M. Wilkinson, B. Mehlig, V. Bezuglyy
Institutions: The Open University, University of Gothenburg
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2041788084