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Master Equation Approach to the Hopping Transport Theory
Author(s) -
Bányai L.,
Aldea A.
Publication year - 1979
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19790270903
Subject(s) - master equation , analogy , perturbation theory (quantum mechanics) , limit (mathematics) , scattering , convection–diffusion equation , statistical physics , physics , perturbation (astronomy) , theoretical physics , mathematics , mathematical analysis , quantum mechanics , epistemology , philosophy , quantum
The fundamentals of the hopping transport theory are analyzed within the Master equation framework, that allows a clarification of the underlying assumptions and approximations. The common nature of the approximations, inherent both in hopping and weak scattering problems, is revealed. Some of the delicate limit problems are illustrated in exactly solvable models. The dangers in applying ordinary perturbation theory to the d.c. conductivity are shown. Through the introduction of the Master equation with external sources a proof of the Miller‐Abrahams resistance‐network analogy is given. There is also a discussion of the “local equilibrium” distribution, with some reference to thermoelectric phenomena.