Time-dependent correlations in the exponential lattice. II. Response functions of the monatomic lattice at low temperatures

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Abstract
A calculation of time-dependent correlations of relative displacements in the linear exponential lattice is presented, based on the analytic approach developed in the preceding paper. The dynamical equations derived for the response functions in wave-vector space are solved numerically, subject to the condition of vanishing external pressure. At very low temperatures the spectral density reveals the familiar phonon response. When the temperature is raised, this structure splits into two peaks in the region of small but not too small wave vectors. The peak which is located at the high-frequency side seems to follow a linear dispersion law. Arguments are presented which identify this peak with high-speed pulselike motions in the chain.