Vector vibrations and the Ioffe-Regel crossover in disordered lattices
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In this article, the spectral density for vector vibrations in the face-centred cubic lattice with force-constant disorder was analyzed within the coherent potential approximation, and the phase diagram showing the weak and strong scattering regimes was presented and compared with that for electrons.Abstract:
The spectral density for vector vibrations in the face-centred cubic lattice with force-constant disorder is analysed within the coherent potential approximation. The phase diagram showing the weak- and strong-scattering regimes is presented and compared with that for electrons. The weak-scattering regime for external long-wavelength vibrational plane waves is shown to be due to sum-rule correlations in the dynamical matrix. A secondary peak below the Brillouin peak for sufficiently large wavevectors is found for the lattice models. The results obtained are supported by precise numerical solutions.read more
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Density of states on fractals : « fractons »
S. Alexander,Raymond Lee Orbach +1 more
TL;DR: In this article, the density of states on a fractal is calculated taking into account the scaling properties of both the volume and the connectivity, and proper mode counting requires a reciprocal space with new intrinsic fracton dimensionality d = 2 d/(2 + δ).
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Localization: theory and experiment
B Kramer,A MacKinnon +1 more
TL;DR: The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day as mentioned in this paper.