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arXiv · 2012.05964

Universal Collective Behavior of the Vibration Spectrum of Highly Connected Disordered Systems

Joshua Feinberg·Roman Riser
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Abstract

We study small oscillations of highly connected systems, which represent a limit opposite to the more familiar case of disordered crystals. As a concrete example we analyze the vibrational spectra of composite pendula. Remarkably, these spectra exhibit universal behavior with non-vanishing zero-frequency limit of the density of phonon states. This universality is captured by a natural random matrix model for such systems. We analyze this model using S-transforms of free probability theory and obtain the density of modes explicitly, in the limit of large system size.

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Joshua Feinberg, Roman Riser. 2020-12-10. Universal Collective Behavior of the Vibration Spectrum of Highly Connected Disordered Systems. https://arxiv.org/abs/2012.05964

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