Analytical expressions for momentum autocorrelation function of a classic diatomic chain

摘要

We use recurrence relations method to study a classical harmonic diatomic chain. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are given in terms of integrals of real and complex elliptic functions for the acoustic and optical branches, respectively. Double convolution results respectively in integrals of trigonometric and hyperbolic functions for expansion coefficients of acoustic and optical branches.