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. Please see the link here: https://stm.bookpi.org/NTPSR-V5/article/view/7163
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