Quantum transport in solids can be defined as the flow of charge or heat under conditions where the movement of the quasiparticles transporting energy through the solid cannot be described at all accurately by classical equations of motion such as the familiar Boltzmann equation. Such conditions may arise when the separation of individual quantum levels becomes comparable with, or greater than, the thermal energy of the carriers or when the particle wavelength becomes of the same order as the sample dimensions or the physical size of the scattering centres.
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R A Stradling (1978) studied this question.