Theory of classical diffusion jumps in solids

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Abstract
A comprehensive new theory of atomic jump processes in classical solids is formulated. Short-term memory is incorporated into the theory for the first time, using properties of the invariant manifolds which occur in the phase spaces of dynamical systems. The results resemble rate theory augmented in such a way that the fate of rapid dynamical fluctuations can be assigned correctly, within the short-memory treatment. For a single barrier it is possible to express the equilibrium jump rate as a ratio of two partition functions, as in simpler theories. The center manifold in phase space replaces the saddle surface in configuration space as the geometrical criterion by which successful jumps can be identified. We provide explicit calculations to compare the jump rates and the mass dependences obtained by use of several alternative jump models.