Time-dependent correlations in the exponential lattice. I. Formal theory of response functions

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Abstract
Time-dependent response functions of classical lattice systems are the object of this study. A general representation for the displacement-displacement response function is presented. In the special case of a linear lattice with exponential interaction potential between adjacent particles this formula leads at low temperatures to a closed system of integrodifferential equations governing the time dependence of the response functions. Thus for this special type of lattice system which supports solutions with strong anharmonic features, a systematic study of dynamical correlations at low temperatures is possible. Numerical results will be presented in the accompanying paper.