The uses of quantum field theory in diffusion-limited reactions

Daniel C. Mattis; M. Lawrence Glasser

doi:10.1103/RevModPhys.70.979

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The uses of quantum field theory in diffusion-limited reactions

Daniel C. Mattis and M. Lawrence Glasser

Daniel C. Mattis

Department of Physics, University of Utah, Salt Lake City, Utah 84112-0830

M. Lawrence Glasser

Departments of Physics and Mathematics, Clarkson University, Potsdam, New York 13699-5820

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Rev. Mod. Phys. 70, 979 – Published 1 July, 1998

DOI: https://doi.org/10.1103/RevModPhys.70.979

Abstract

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.

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The uses of quantum field theory in diffusion-limited reactions

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