在超流体的表面
On the surface of superfluids
摘要：
本文在最近关于普通相对论流体局域泡的工作的基础上，研究了相对论超流体在$3+1$和$2+1$维中耦合到任意定常背景度规和规范场的相对论超流体的相对丰富的首阶表面物理。分析是在一个较低的维度，写在超流戈德斯通模式，形状场（表征表面的超流气泡）和背景领域的欧几里得有效作用的帮助下进行的。我们发现新的条款在理想的超流表面的本构关系，在奇偶偶和奇偶奇部门，与相应的输运系数完全固定的一阶散装输运系数。一些整体输运系数甚至进入并修改表面热力学。在这个过程中，我们还评估了固定的一阶奇偶奇体电流在$2+1$尺寸，这是从四个独立的条款在该部门的超流有效行动。在本文的第二部分中，我们通过对$4+1$维零超流体的零约化，将我们的分析推广到了$3+1$维伽利略超流体中的稳态表面。理想序本构关系在伽利略情况下也表现出一些新的条款，类似于他们的相对论性对应。最后，在相对论的背景下，我们打开缓慢但任意的时间依赖性，并回答一些关键问题的形状场的依赖于时间的动力学使用热力学第二定律。对玩具平衡位形进行了$2+1$维线性涨落分析，揭示了一些新的表面模式，包括奇偶奇模。我们的框架可以很容易地应用到不同的流体相之间的更一般的接口模型。
英文摘要：
Developing on a recent work on localized bubbles of ordinary relativistic fluids, we study the comparatively richer leading order surface physics of relativistic superfluids, coupled to an arbitrary stationary background metric and gauge field in $3+1$ and $2+1$ dimensions. The analysis is performed with the help of a Euclidean effective action in one lower dimension, written in terms of the superfluid Goldstone mode, the shape-field (characterizing the surface of the superfluid bubble) and the background fields. We find new terms in the ideal order constitutive relations of the superfluid surface, in both the parity-even and parity-odd sectors, with the corresponding transport coefficients entirely fixed in terms of the first order bulk transport coefficients. Some bulk transport coefficients even enter and modify the surface thermodynamics. In the process, we also evaluate the stationary first order parity-odd bulk currents in $2+1$ dimensions, which follows from four independent terms in the superfluid effective action in that sector. In the second part of the paper, we extend our analysis to stationary surfaces in $3+1$ dimensional Galilean superfluids via the null reduction of null superfluids in $4+1$ dimensions. The ideal order constitutive relations in the Galilean case also exhibit some new terms similar to their relativistic counterparts. Finally, in the relativistic context, we turn on slow but arbitrary time dependence and answer some of the key questions regarding the time-dependent dynamics of the shape-field using the second law of thermodynamics. A linearized fluctuation analysis in $2+1$ dimensions about a toy equilibrium configuration reveals some new surface modes, including parity-odd ones. Our framework can be easily applied to model more general interfaces between distinct fluid-phases.
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