From the Kubo formula to variable range hopping

Abstract

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.

5 pages, published version with an extended concluding paragraph

References in corpus (7)

• Dynamic response of isolated Aharonov-Bohm rings coupled to an electromagnetic resonator
• Conductance of Aharonov--Bohm Rings: From the Discrete to the Continuous Spectrum Limit
• Semilinear Response
• Rate of energy absorption by a closed ballistic ring
• Correlations in the Adiabatic Response of Chaotic Systems
• The conductance of a multi-mode ballistic ring: beyond Landauer and Kubo
• The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

Cited by in corpus (4)

• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture
• Random-matrix modeling of semi-linear response, the generalized variable range hopping picture, and the conductance of mesoscopic rings
• Diffusion in sparse networks: linear to semi-linear crossover
• Energy absorption by "sparse" systems: beyond linear response theory