Abstract
A classical harmonic oscillator chain with alternating masses is studied using the recurrence relations method. The momentum autocorrelation function changes from combination of cosines to Bessel functions when the number of oscillators increases from finite to infinite bringing about irreversibility. Optic and acoustic branches of the momentum autocorrelation function are expanded in terms of even-order Bessel functions and are shown to be finite and well behaved. Irreversibility and ergodicity are discussed.
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