Lattice diffusion and the Heisenberg ferromagnet

Abstract
It is shown that the master equation for a general diffusion problem with exclusion and symmetric binary transfer rates can be mapped exactly on the Schrödinger equation for an equivalent Heisenberg ferromagnet. Quantities of physical interest, e.g., the site occupation probability, are related to the lowest eignstates of the ferromagnet which play no thermodynamic role. The thermodynamics is only reflected in unobservable quantities such as the joint occupation probability of all sites. An additional result, obtained by elementary considerations, is the exact equation for the time evolution of the site-occupation probabilities. For symmetric transfer rates the equation reduces to a linear form in which exclusion effects are no longer present.

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