理想分形子超流体
Ideal fracton superfluids
AI总结：
本研究针对分形子对称系统的平衡热态构建问题，通过规范分形子代数引入两类分形子超流体并分析其流体力学模式，发现其独特特征并统一了此前相关研究，拓展了分形子系统的热力学理论。
摘要：
我们研究了任意弯曲空间中具有分形子对称性的系统的平衡热态热力学及其近平衡动力学。通过显式规范分形子代数，我们得到了具有守恒偶极矩的场论所耦合的几何与规范场。我们利用所得的分形子几何证明，除非部分分形子对称性自发破缺，否则无法为全局热态构建平衡配分函数。这促使我们引入两类具有守恒能量和动量的分形子超流体，即$p$波和$s$波分形子超流体。后者在理想阶是亚里士多德超流体，但带有速度约束，且可分为两个不同的区域：U(1)分形子超流体区和钉扎$s$波超流体区。针对这些类别和区域，我们分别构建了流体力学展开并研究了由此产生的模式。我们在不引入耗散效应的情况下，在梯度的理想阶发现了每个相和区域的独特特征，尤其注意到$s$波分形子超流体中存在声模。我们表明，此前关于分形子流体力学的研究可归入这些类别。最后，除了研究理想亚里士多德超流体的热力学外，我们还研究了具有大动质量的超高密度$p$波分形子超流体。
英文摘要：
We investigate the thermodynamics of equilibrium thermal states and their near-equilibrium dynamics in systems with fractonic symmetries in arbitrary curved space. By explicitly gauging the fracton algebra we obtain the geometry and gauge fields that field theories with conserved dipole moment couple to. We use the resultant fracton geometry to show that it is not possible to construct an equilibrium partition function for global thermal states unless part of the fractonic symmetries is spontaneously broken. This leads us to introduce two classes of fracton superfluids with conserved energy and momentum, namely $p$-wave and $s$-wave fracton superfluids. The latter phase is an Aristotelian superfluid at ideal order but with a velocity constraint and can be split into two separate regimes: the U(1) fracton superfluid and the pinned $s$-wave superfluid regimes. For each of these classes and regimes we formulate a hydrodynamic expansion and study the resultant modes. We find distinctive features of each of these phases and regimes at ideal order in gradients, without introducing dissipative effects. In particular we note the appearance of a sound mode for $s$-wave fracton superfluids. We show that previous work on fracton hydrodynamics falls into these classes. Finally, we study ultra-dense $p$-wave fracton superfluids with a large kinetic mass in addition to studying the thermodynamics of ideal Aristotelian superfluids.
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