Quantization of the elastic modes in an isotropic plate
T. K\"uhn, D. V. Anghel
TL;DR
This paper develops a method to quantize elastic phonon modes in an isotropic plate by deriving a complete set of orthogonal eigenfunctions, aiding the understanding of low-temperature behaviors in ultra-thin membranes.
Contribution
It introduces a comprehensive approach to quantize elastic modes in plates, providing explicit eigenfunctions and dispersion relations for phonon analysis.
Findings
Complete orthogonal eigenfunctions derived
Normalized elastic modes established
Dispersion relations characterized
Abstract
We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion relations are manifested in low temperature experiments in ultra-thin membranes.
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