标题： 一维卡罗尔流体 I：卡罗尔-伽利略对偶 显示英文标题

标题： One-dimensional Carrollian fluids I: Carroll-Galilei duality

摘要： 伽利略代数和卡罗尔代数在二维牛顿-卡坦流形和卡罗尔流形上是同构的。 这一性质的一个结果是，一维伽利略流体和卡罗尔流体之间存在对偶对应关系。 我们描述了这些系统从洛伦兹流体力学相关极限中出现的动力学，并探讨了所提到的对偶关系。 这会交换流动速度方向上的纵向和横向，并置换平衡和非平衡可观测量，揭示了卡罗尔物理的具体特征。 我们研究了局部流体力学框架变换在伽利略和卡罗尔配置中的作用，即对偶的伽利略和卡罗尔局部提升，并评论了它们的潜在破坏。 重点放在为了在牛顿-卡坦和卡罗尔时空内获得完整的流体力学方程组所必需的额外几何元素上。 我们的分析是在一般的卡坦框架以及更明确的坐标系中进行的，这些坐标系特别适用于伽利略或卡罗尔使用。 显示英文摘要

摘要： Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe the dynamics of these systems as they emerge from the relevant limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. We investigate the action of local hydrodynamic-frame transformations in the Galilean and Carrollian configurations, i.e. dual Galilean and Carrollian local boosts, and comment on their potential breaking. Emphasis is laid on the additional geometric elements that are necessary to attain complete systems of hydrodynamic equations in Newton-Cartan and Carroll spacetimes. Our analysis is conducted in general Cartan frames as well as in more explicit coordinates, specifically suited to Galilean or Carrollian use.