A monatomic chain with an impurity in mass and Hooke constant

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 p...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2019-12, Vol.92 (12), Article 272
Main Author: Yu, Ming B.
Format: Article
Language:English
Subjects:
Autocorrelation functions
Bessel functions
Chains
Complex Systems
Condensed Matter Physics
Convolution
Correlation analysis
Fluid- and Aerodynamics
Impurities
Momentum
Physics
Physics and Astronomy
Poles
Regular Article
Solid State Physics
Trigonometric functions
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Summary: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. Graphical abstract
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2019-100383-1