Exotic Acoustic-Edge and Thermal Scaling in Disordered Hyperuniform Networks
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911239125336064 |
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| author | Jiao, Yang |
| author_facet | Jiao, Yang |
| contents | We develop a first-principles theory for the vibrational density of states (VDOS) and thermal properties of network materials built on stationary correlated disordered point configurations. For scalar (mass--spring) models whose dynamical matrix is a distance-weighted graph Laplacian, we prove that the limiting spectral measure is the pushforward of Lebesgue measure by a Fourier symbol that depends only on the edge kernel \(f\) and the two-point statistics \(g_2\) (equivalently the structure factor \(S\)). For hyperuniform systems with small-$k$ scaling \(S(k)\sim k^α\) and compensated kernels, {the VDOS exhibits an algebraic \emph{pseudogap} at low frequency, \(g(ω)\sim ω^{\,2d/β-1}\) with \(β=\min\{4,α+2\}\), which implies a low-temperature specific heat \(C(T)\sim T^{\,2d/β}\) and a heat-kernel decay \(Z(t)\sim t^{-d/β}\), defining a spectral dimension \(d_s=2d/β\).} This hyperuniformity-induced algebraic edge depletion could enable novel wave manipulation and low-temperature applications. Generalization to vector mechanical models and implications on material design are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exotic Acoustic-Edge and Thermal Scaling in Disordered Hyperuniform Networks Jiao, Yang Soft Condensed Matter Statistical Mechanics We develop a first-principles theory for the vibrational density of states (VDOS) and thermal properties of network materials built on stationary correlated disordered point configurations. For scalar (mass--spring) models whose dynamical matrix is a distance-weighted graph Laplacian, we prove that the limiting spectral measure is the pushforward of Lebesgue measure by a Fourier symbol that depends only on the edge kernel \(f\) and the two-point statistics \(g_2\) (equivalently the structure factor \(S\)). For hyperuniform systems with small-$k$ scaling \(S(k)\sim k^α\) and compensated kernels, {the VDOS exhibits an algebraic \emph{pseudogap} at low frequency, \(g(ω)\sim ω^{\,2d/β-1}\) with \(β=\min\{4,α+2\}\), which implies a low-temperature specific heat \(C(T)\sim T^{\,2d/β}\) and a heat-kernel decay \(Z(t)\sim t^{-d/β}\), defining a spectral dimension \(d_s=2d/β\).} This hyperuniformity-induced algebraic edge depletion could enable novel wave manipulation and low-temperature applications. Generalization to vector mechanical models and implications on material design are also discussed. |
| title | Exotic Acoustic-Edge and Thermal Scaling in Disordered Hyperuniform Networks |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2510.25136 |