Generalised transport method and applications

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Abstract
The theory of electrical conductivity is examined within the projection operator formalism and contact is made with the proper connected-diagram expansion method. A close similarity between the two formalisms is found to exist, although the diagrammatic analysis of the superoperator resolvent is found to be more general and amenable to reasonable physical interpretation. Using the projection operator calculus, it is shown that the explicit choice of the time memory function changes the transport characteristics, an effect unreachable by the Boltzmann or Pauli equation, and the frequency dependent formula for one-dimensional diffusive conductivity is derived. Broadening of the cyclotron resonance spectra on the semiconductor surfaces is obtained by employing the proper connected diagram expansion of the superoperator resolvent for the case when the quantum jumps made by the electron are interrupted at random by the perturbing fields of the impurities and the surface phonons.