The uses of quantum field theory in diffusion-limited reactions

The techniques of quantum field theory on a lattice are used to examine the diffusion and reaction processes of particles in a solid, such as vacancies or interstitials, or chemical species of all kinds which move by discrete random hopping processes and react in a prescribed way when they are in proximity. First formulated by Doi in the 1970s, the quantum-field-theoretic solution of the “master equation” of statistical physics allows a systematic investigation of any number of nonequilibrium processes ranging from fluorescence to explosions. By formulating the problem on the points of a space lattice in $d$ dimensions one can control the ultraviolet divergences associated with short-range interactions. For illustrative purposes several models are solved in detail. The authors include as an appendix a chronological list of seminal articles in the field.