Diffusion and universal relaxation of holographic phonons
arXiv:1904.11445 · doi:10.1007/JHEP10(2019)068
Abstract
In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data {of the dual background black hole solution}. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent . Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solids.
arXiv commentv3: Typos fixed, discussion improved, version published in JHEP. v2: minor typos fixed, references added. v1: 24 pages plus appendices, contains an extended discussion of parts of arXiv:1812.08118 as well as new material
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