Sound Topology, Duality, Coherence and Wave-Mixing by Pierre Deymier & Keith Runge

Author:Pierre Deymier & Keith Runge
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In this image, the satellite peaks coincide with discrete, near-resonance modes. The central peak frequencies of modes k ′ and k ′′ add (or subtract) to yield satellite peaks to the central peak for k ∗ = π/a. The primary satellite peaks at 1.999 and 1.969 rad/s come from Case I. The secondary satellite peaks at 2.015 and 1.951 rad/s come from Case II. Tertiary, quaternary and other higher order satellite peaks exist and are revealed if the scale on the right hand SED plot is adjusted. The magnitude of the satellite peaks depends upon the “distance” from the central peak at k = π/a in accordance with their near resonant character. This distance depends upon the size of the MD simulation. For an MD simulation with N = 100 atoms, there are 51 discrete, non-degenerate wave vector modes available between the center of the irreducible Brillouin zone and the zone edge. For N = 1000 atoms, there are 501 available modes. The resolution in wave vector space is finer for larger MD systems as is the resolution in frequency space. Higher frequency resolution results in smaller spacing between satellite peaks. This is shown in Fig. 4.7. As the number of atoms (N) increases, the satellite peaks congregate around the central peak and increase in relative amplitude. In the limit of an infinite system all satellite peaks merge into the central peak.

Fig. 4.7SED-frequency plots for 1D anharmonic monatomic crystal at k = π/a for MD systems of varying sizes. The parameter characterizing the degree of anharmonicity in the 1D crystal is ε = 3.0

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