Hydrodynamics of disordered marginally-stable matter

Abstract

We study the vibrational spectra and the specific heat of disordered systems using an effective hydrodynamic framework. We consider the contribution of diffusive modes, i.e. the 'diffusons', to the density of states and the specific heat. We prove analytically that these new modes provide a constant term to the vibrational density of states $g(\omega )$. This contribution is dominant at low frequencies, with respect to the Debye propagating modes. We compare our results with numerical simulations data and random matrix theory. Finally, we compute the specific heat and we show the existence of a linear in $T$ scaling $C(T)\sim cT$ at low temperatures due to the diffusive modes. We analytically derive the coefficient $c$ in terms of the diffusion constant $D$ of the quasi-localized modes and we obtain perfect agreement with numerical data. The linear in $T$ behavior in the specific heat is stronger the more localized the modes, and crosses over to a $T^3$ (Debye) regime at a temperature $T^{\ast }\sim \sqrt{v^3/D}$, where $v$ is the speed of sound. Our results suggest that the anomalous properties of glasses and disordered systems can be understood effectively within a hydrodynamic approach which accounts for diffusive quasi-localized modes generated via disorder-induced scattering.

arXiv commentv2: 5 pages, 5 figures, minor revision, matching the published version in PRResearch as Rapid Communication

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• Stringlet Excitation Model of the Boson Peak
• A new paradigm for the low-T glassy-like thermal properties of solids
• Emergence of two-level systems in glass formers: a kinetic Monte Carlo study
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• Dynamics of Disordered Mechanical Systems with Large Connectivity, Free Probability Theory, and Quasi-Hermitian Random Matrices
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• Physics of Phonon-Polaritons in Amorphous Materials
• Universal superdiffusive modes in charged two dimensional liquids
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• Temperature crossovers in the specific heat of amorphous magnets