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arXiv · 2603.26825

Anomalous phonon dispersion near yielding in athermal crystals

Fumiaki Nakai·Michio Otsuki·Kuniyasu Saitoh·Hiroaki Katsuragi
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Abstract

Vibrational properties of ordered athermal solids near yielding remain poorly understood. We show that yielding in a sheared crystal is governed not by a single localized instability but by directionally extended multimode softening that forms a cross-shaped low-frequency region in wave number space. Near yielding, the acoustic dispersion $\omega\sim k$ is replaced by $\omega\sim k^2$ along the soft direction, and the vibrational density of states crosses over from Debye to non-Debye scaling, with a diverging length scale. We analytically derive these scaling laws.

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Fumiaki Nakai, Michio Otsuki, Kuniyasu Saitoh, Hiroaki Katsuragi. 2026-03-27. Anomalous phonon dispersion near yielding in athermal crystals. https://doi.org/10.1103/3lnj-1ml1

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