One-Dimensional Magnetic Atom Chain Forged
One-Dimensional Magnetic Atom Chain Forged
Aug 4, 2016
ieee.org
4.2 Write down the dynamic equation for a one-dimensional linear chain ofN (large number) atoms (atomic distance a, restoring force f, atomic massm) and solve this with an ansatz un(t) = u(q) [i(qna-ω t)].a) Compare the obtained dispersion ω(q) with that of the diatomic linearchain (4.15).Nb) Show that the total momentum ∑n=1^N m u̇n(t) of a phonon vanishes.c) Show that for long wavelengths (q ≪ a^-1) the dynamic equation for thechain transforms into a wave equation for elastic waves when the di
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