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.

We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.

Expressions for spin wave energies in normal and inverse spinel have been obtained which are exact to all orders in the spin wave momentum. These dispersion curves have been compared with existing experimental data on magnetite and good agreement found if the principal exchange interaction is taken to be 2.4×${10}^{-3\mathrm{}}$ eV. The surprisingly small range of validity of the usual $k^2$ approximation is pointed out and possible effects of the deviation from $k^2$ behavior on the magnetic part of the heat capacity are discussed. The small (like-like) exchange interactions have been included (also to all orders in the spin-wave momentum) with the most important result that agreement with the experimental dispersion curves is improved.