Regular Article

A monatomic chain with an impurity in mass and Hooke constant

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Received: 2 August 2019
Received in final form: 12 October 2019
Published online: 18 December 2019

Abstract

A classical monatomic chain with an impurity in both mass and Hooke constant is studied by means of the recurrence relations method. The momentum autocorrelation function of the impurity is contributed by resonant poles and a branch cut. Though the model has two pairs of poles but only one pair is physical and contributes a cosine to the momentum autocorrelation function, whose frequency and amplitude are derived. The cut contribution is given by a convolution product of a sine and a sum of two Bessel functions of zeroth and second order. The memory function of the model is also derived which is contributed by a pair of poles and a branch cut. The former gives a cosine and the latter a convolution of a sine and a sum of two Bessel functions. The ergodicity of the momentum of the impurity is also discussed.