Abstract
Exact calculations are presented which detail the process of polaron formation in the one-dimensional acoustic chain. Exact solution is possible because the limit considered is the transportless limit in which the Hamiltonian matrix elements responsible for the motion of an excitation among site states have been set to zero. The polaron formation process is found to be decomposable into two subprocesses having distinct time scales. A disparity of time scales is possible in the case of long wavelength excitations. The consistency of our conclusions is demonstrated through the consensus of results obtained for the discrete acoustic chain, the Debye model, and the elastic continuum.
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