Gapped momentum states

Abstract

Important properties of a particle, wave or a statistical system depend on the form of a dispersion relation (DR). Two commonly-discussed dispersion relations are the gapless phonon-like DR and the DR with the energy or frequency gap. More recently, the third and intriguing type of DR has been emerging in different areas of physics: the DR with the gap in momentum, or k-space. It has been increasingly appreciated that gapped momentum states (GMS) have important implications for dynamical and thermodynamic properties of the system. Here, we review the origin of this phenomenon in a range of physical systems, starting from ordinary liquids to holographic models. We observe how GMS emerge in the Maxwell-Frenkel approach to liquid viscoelasticity, relate the k-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space and vice versa. We subsequently discuss how GMS emerge in the two-field description which is analogous to the quantum formulation of dissipation in the Keldysh-Schwinger approach. We discuss experimental evidence for GMS, including the direct evidence of gapped Email addresses: matteo.baggioli@uam.es (Matteo Baggioli), professorvasin@gmail.com (Mikhail Vasin), brazhkin@hppi.troitsk.ru (Vadim Brazhkin), k.trachenko@qmul.ac.uk (Kostya Trachenko)DR coming from strongly-coupled plasma. We also discuss GMS in electromagnetic waves and non-linear Sine-Gordon model. We then move on to discuss the recently developed quasihydrodynamic framework which relates the k-gap with the presence of a softly broken global symmetry and its applications. Finally, we review recent discussions of GMS in relativistic hydrodynamics and holographic models. Throughout the review, we point out essential physical ingredients required by GMS to emerge and make links between different areas of physics, with the view that new and deeper understanding will benefit from studying the GMS in seemingly disparate fields and from clarifying the origin of potentially similar underlying physical ideas and equations. Keywords:12 Dispersion relations resulting from solving (56) for different τ c : (a) τ c = 5, (b) τ c = 0.58, (c) τ c = 0.54, (d) τ c = 0.51, (e) τ c = 0.4

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

“…We show our results in fig.6. We observe that, for small values of the dimensionless parameter m/T , the two modes collide at an initial value of momentum k 1 , creating a finite real part in a k−gap fashion [51]. Nevertheless, at a second value of the momentum k 2 > k 1 the modes split up and the real part becomes zero.…”

“…This is motivated by the interesting features observed in the solid version of the model [49,50]. In particular it is plausible that this model also exhibits the so-called k−gap phenomenon [51], namely the appearance of a propagating shear wave beyond a certain momentum k > k g . First, we give a snapshot of the first four modes in the spectrum at a specific value of m/T in fig.5.…”

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.…”

Transverse collective modes in interacting holographic plasmas

“…The residual damping at k = 0 is natural in holographic models due to the absence of quasi-particles, and the related appearance of an incoherent critical continuum of excitations, leading to the experimentally observed featureless nature of plasmons in strange metals [4,5]. Furthermore, the possibility of having new dispersion relations, especially linked to the k-gap phenomenon [15][16][17][18][19], has been discussed [8,13].…”