Study about Diatomic Chain with a Mass Impurity


The recurrence relations approach is used to investigate how an impurity influences a harmonic oscillator chain. A standard diatomic chain with one mass impurity is analysed. Two pairs of resonant poles and three branch cuts provide the impurity’s momentum Autocor- relation function. The pole contribution is provided by cosine(s), whereas the cut contribution is provided by the acoustic and optic branches. The extension of even-order Bessel functions is used to express both branches. For the acoustic branch, the expansion coefficients are integrals of Jacobian elliptic functions along the real axis in a complex plane, and for the optical branch, integrals along a contour parallel to the imaginary axis. The estimated pole and cut contributions show how the mass impurity affects the mass impurity’s momentum autocorrelation function in a typical diatomic chain, and so give greater insight into the mass impurity’s momentum autocorrelation function.

Author(s) Details:

Ming B. Yu,
8000 Badura Ave. Unit 1053, Las Vegas, NV. 89113, USA.

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