Low frequency propagating shear waves in holographic liquids

Journal of High Energy Physics, Mar 2019

Abstract Recently, it has been realized that liquids are able to support solid-like transverse modes with an interesting gap in momentum space developing in the dispersion relation. We show that this gap is also present in simple holographic bottom-up models, and it is strikingly similar to the gap in liquids in several respects. Firstly, the appropriately defined relaxation time in the holographic models decreases with temperature in the same way. More importantly, the holographic k-gap increases with temperature and with the inverse of the relaxation time. Our results suggest that the Maxwell-Frenkel approach to liquids, involving the additivity of liquid hydrodynamic and solid-like elastic responses, can be applicable to a much wider class of physical systems and effects than thought previously, including relativistic models and strongly-coupled quantum field theories. More precisely, the dispersion relation of the propagating shear waves is in perfect agreement with the Maxwell-Frenkel approach. On the contrary the relaxation time appearing in the holographic models considered does not match the Maxwell prediction in terms of the shear viscosity and the instantaneous elastic modulus but it shares the same temperature dependence.

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Low frequency propagating shear waves in holographic liquids

Journal of High Energy Physics March 2019, 2019:93 | Cite as Low frequency propagating shear waves in holographic liquids AuthorsAuthors and affiliations Matteo BaggioliKostya Trachenko Open Access Regular Article - Theoretical Physics First Online: 15 March 2019 40 Downloads Abstract Recently, it has been realized that liquids are able to support solid-like transverse modes with an interesting gap in momentum space developing in the dispersion relation. We show that this gap is also present in simple holographic bottom-up models, and it is strikingly similar to the gap in liquids in several respects. Firstly, the appropriately defined relaxation time in the holographic models decreases with temperature in the same way. More importantly, the holographic k-gap increases with temperature and with the inverse of the relaxation time. Our results suggest that the Maxwell-Frenkel approach to liquids, involving the additivity of liquid hydrodynamic and solid-like elastic responses, can be applicable to a much wider class of physical systems and effects than thought previously, including relativistic models and strongly-coupled quantum field theories. More precisely, the dispersion relation of the propagating shear waves is in perfect agreement with the Maxwell-Frenkel approach. On the contrary the relaxation time appearing in the holographic models considered does not match the Maxwell prediction in terms of the shear viscosity and the instantaneous elastic modulus but it shares the same temperature dependence. Keywords Holography and condensed matter physics (AdS/CMT) Gauge-gravity correspondence AdS-CFT Correspondence Black Holes in String Theory  ArXiv ePrint: 1807.10530 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Second Edition: Volume 6 (Course of Theoretical Physics), 2 edition, Butterworth-Heinemann (1987).Google Scholar [2] L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Vol. 7, Theory of Elasticity, Pergamon Press (1970).Google Scholar [3] P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press (1995).Google Scholar [4] F.H. MacDougall, Kinetic theory of liquids. By J. Frenkel., J. Phys. Chem. 51 (1947) 1032.Google Scholar [5] K. 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Matteo Baggioli, Kostya Trachenko. Low frequency propagating shear waves in holographic liquids, Journal of High Energy Physics, 2019, 93, DOI: 10.1007/JHEP03(2019)093