The motion of a light particle in a solid, coupled to conduction electrons and/or phonons, was investigated within the framework of a 2-state model. This could be taken to represent the particle ground states in 2 neighboring potential wells. An important distinction arose with regard to the coupling of the particle to phonons. This distinction existed between special 2-phonon processes (so-called di-phonon processes), which resulted from non-linear particle-lattice coupling and could give rise to quasi-elastic phase-destroying scattering, and essentially inelastic processes which could arise from linear as well as non-linear particle-lattice coupling. An important parameter which affected particle motion was the static energy shift between the particle ground states in the 2 wells. The 2-state model permitted reliable estimates to be made of the boundary in the energy shift versus temperature plane which separated the regimes of incoherent hopping from those of coherent band-like motion. Within the regime of incoherent motion, a number of sub-regimes could exist. The situation became particularly interesting when condensation of the electron system took, as in the case of a Bardeen-Cooper-Schriefer superconductor. It was then necessary to distinguish the domains within which the hopping rates were dominated by either quasi-particle coupling, di-phonon processes, 1-phonon processes, Cooper-pair breaking, coupling to normal conducting electrons, or multi-phonon assisted processes. In the case of a series of light particles which carried 1 positive elementary charge, and included the positive muon and the nuclei of H isotopes, the range of validity of the 2-state description extended to relatively high temperatures for + but only to rather lower temperatures in the case of heavier particles.

T.Regelmann, L.Schimmele, A.Seeger: Philosophical Magazine B, 1995, 72[2], 209-32