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A simple exact solution of the incommensurate chain with infinite-range interactions is obtained with the use of both analytic and graphical techniques. The ground states and all metastable states are identified. Results are derived for the depinning transition, the sliding threshold, and the excitation spectrum as a function of pinning strength and applied field. The ac response is also obtained and has a low-frequency singularity at threshold, but the dielectric constant is bounded, as seen in charge-density-wave experiments.
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Leigh Sneddon (1984) studied this question.
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