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 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.

中文翻译：

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缺口动量状态

粒子、波或统计系统的重要属性取决于色散关系 (DR) 的形式。两种经常讨论的色散关系是无间隙的类声子 DR 和具有能量或频率间隙的 DR。最近，在物理学的不同领域出现了第三种有趣的 DR：具有动量间隙的 DR，或 $k$-空间。人们越来越意识到间隙动量状态 (GMS) 对系统的动力学和热力学性质具有重要意义。在这里，我们回顾了这种现象在一系列物理系统中的起源，从普通液体到全息模型。我们观察了 GMS 如何在 Maxwell-Frenkel 方法中出现的液体粘弹性，将 $k$-gap 与耗散联系起来，并观察 DR 中的差距如何从能量空间到动量空间不断变化，反之亦然。我们随后讨论 GMS 如何出现在类似于 Keldysh-Schwinger 方法中耗散的量子公式的双场描述中。我们讨论了 GMS 的实验证据，包括来自强耦合等离子体的间隙 DR 的直接证据。我们还讨论了电磁波和非线性 Sine-Gordon 模型中的 GMS。然后我们继续讨论最近开发的准流体动力学框架，该框架将 $k$-gap 与软破坏全局对称性的存在及其应用联系起来。最后，我们回顾了 GMS 在相对论流体动力学和全息模型中的最新讨论。在整个审查过程中，