Low frequency propagating shear waves in holographic liquids

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 stronglycoupled 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.

Zoology of solid & fluid holography — Goldstone modes and phase relaxation

“…In case of EXB (section 3), the dynamics of the fluid model at small frequencies and momenta (ω/T, k/T 1) is very similar to the solids described in [45]. Both a k−gap phenomenon [49] and a coherent-incoherent transition [46] appear. Nevertheless, the fluid model displays a more complex structure beyond the hydrodynamic limit, which is due to its higher derivative nature compared to the solid counterpart.…”

Transverse collective modes in interacting holographic plasmas

“…A finite charge density leads to several consequences for the k-gap dynamics: Firstly, the hydrodynamic charge diffusion mode is given a finite damping at k = 0, and therefore ceases to be a hydrodynamic mode in the strict sense. The situation is analogous to what happens in the spectrum of the linear axion model [25] once translations are broken [17,18]. Secondly, the position of the momentum gap moves towards lower momenta, until approaching the origin and being converted to a real frequency/energy gap (a mass) (see [35] for a field theory analysis).…”

Viscoelastic hydrodynamics and holography

“…It would be interesting to consider such extensions as it can aid in the understanding of recent holographic studies [50,68,69]. It is natural to consider the works [29,32,33,37,38] and charged generalisations [50,68,69] within the framework of generalised global symmetries. We would also like to understand whether sec.…”

“…Two types of models have been considered in the literature: gravity coupled to a set of scalar fields Φ I [30,31,33] (and with additional fields [31,32]) and gravity minimally coupled to a set of higher-form gauge fields B I [22]. The former is supposed to describe the dynamics of viscoelastic materials with spontaneously broken translation symmetries while the latter is supposed to describe viscoelastic theories with higher-form currents (see also [37,38]). However, the establishment of a precise map between the two hydrodynamic formulations has prompt us to investigate whether such a map exists at the level of holographic models.…”