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The compacting of a column of grains has been studied using a one-dimensionalIsing model with long range directed interactions in which down and up spinsrepresent orientations of the grain having or not having an associated void.When the column is not shaken (zero 'temperature') the motion becomes highlyconstrained and under most circumstances we find that the generator of thestochastic dynamics assumes an unusual form: many eigenvalues becomedegenerate, but the associated multi-dimensional invariant spaces have but asingle eigenvector. There is no spectral expansion and a Jordan form must beused. Many properties of the dynamics are established here analytically; someare not. General issues associated with the Jordan form are also taken up.

Spectral properties of zero temperature dynamics in a model of a compacting granular column