Quantum Mechanical Theory of Hydrogen Diffusion

A quantum mechanical description of low-concentration hydrogen diffusion is presented. Using the Kubo formula for the diffusion coefficent, harmonic wave functions for the hydrogen atoms, and polaronic wave functions for the lattice, an exact expression for the diffusion coefficent can be found. Two interesting predictions of the theory are (i) a decrease in the activation energy with mass for fcc metals, in agreement with experiment, and (ii) an activated form for diffusion between localized states even in the purely tunneling regime.