Exponential Fourier Transforms for Coupled Harmonic Oscillator Chains

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Abstract
The exponential Fourier transform is used to study the dynamics of semi‐infinite and infinite chains of interacting harmonic oscillators. In addition to the harmonic coupling between nearest neighbors, each oscillator is subjected to frictional and other external time‐dependent forces. In contrast with previous studies on such systems, the initial conditions (at t = 0) are not specified, and the motion of all the oscillators is expressed in terms of the given applied forces only. The analytic structure of the transforms as well as some properties of the propagators are studied for all possible values of physical constants including the limiting values for uncoupled oscillators. The inverse transforms not readily available from tables are obtained by carrying out the integrations explicitly.

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