From the Kubo formula to variable range hopping

Details From the Kubo formula to variable range hopping From the Kubo formula to variable range hopping

2006-11-27

arxiv.org/abs/cond-mat/0611663v3

Phys. Rev. B 75, 125316 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages, published version with an extended concluding paragraph

Scientific paper

10.1103/PhysRevB.75.125316

Consider a multichannel closed ring with disorder. In the semiclassical treatment its conductance is given by the Drude formula. Quantum mechanics challenge this result both in the limit of strong disorder (eigenstates are not quantum-ergodic in real space) and in the limit of weak disorder (eigenstates are not quantum-ergodic in momentum space). Consequently the analysis of conductance requires going beyond linear response theory, leading to a resistor network picture of transitions between energy levels. We demonstrate that our semi-linear response theory provides a firm unified framework from which the "hopping" phenomenology of Mott can be derived.

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