Energy transfer in one-dimensional substitutionally disordered systems. I. The effects of coherence, tunneling, and thermal promotion

A theory for energy transfer in substitutionally disordered solids is presented that includes the effects of coherent and incoherent migration of the wave packet, the statistical distribution of fluctuations in the potential energy surface the wave packet encounters, and tunneling. Explicit expressions for the ’’diffusion’’ coefficient in these limits and the energy-partitioning ratios in binary systems are derived. It is also shown that an activation energy dependent upon the composition of the binary system can emerge from such a treatment and is an indication that energy transfer between localized states is facilitated by concurrent tunneling and thermal promotion.