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

2020/12/10 by Joshua Feinberg, Feinberg, Joshua, Roman Riser +1
Agricultural and Biological Sciences · #Advanced Scientific Research Methods #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2012.05964

openalex publication_date 2020/12/10 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28

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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