Spin diffusion on a lattice: Classical simulations and spin coherent states

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Abstract
The results of computational studies of classical spin diffusion on a lattice are presented, and the validity of these results in the quantum regime is explored using a general theoretical framework. First, classical simulations of spin diffusion are used to identify conservation principles required for adherence to a traditional diffusion equation. The breakdown of diffusive behavior for magnetization in zero applied field is tied to nonconservation of spin angular momentum by the dipole-dipole interaction. The effects of dilution upon the spin diffusion constant are also studied for lattices of various dimensionalities. At low concentrations and low dimensionality, the results are suggestive of percolation. Next, with considerations of spin diffusion serving as a model, classical spin dynamics on a lattice are linked to quantum dynamics using the interpolating properties of spin coherent states. For systems with initial disturbances characterized by slow spatial variation, and in the limit of high temperature and large particle number, and a full quantum treatment of the spin diffusion problem is shown to reduce to the classical paradigm used in numerical simulations. The equivalence of quantum and classical behaviors under these conditions is shown to result from the cancellation of quantum interference terms in the coherent-state representations of expectation values.