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arXiv · 1601.05566

Hearing the Symmetries of Crystal Lattices from the Integrated Acoustic Spectrum

B. Honari·H. Mohades
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Abstract

Let $C$ be a crystal and $\phi$ be a periodic realization of it in $\mathbb{R}^n$, also let $L$ be the lattice group of $\phi(C)$ which preserves the covering space nature of crystal lattices. In this article, firstly, we define the concept of acoustic spectrum of the crystal lattice C and then provide the algebraic formalism of the question of finding the frequencies of the torus $\mathbb{R}^n/L$, when the set of acoustic spectrum is known. An answer for crystals with uniform atomic force constants is given.

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B. Honari, H. Mohades. 2016-01-21. Hearing the Symmetries of Crystal Lattices from the Integrated Acoustic Spectrum. https://arxiv.org/abs/1601.05566

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