全息超流体中与超固体有关的现象：椭圆余弦波
Supersolidity-related phenomena in holographic superfluid: cnoidal wave
摘要：
首次在有限温度全息超流模型中研究了类超固态的候选者椭圆余弦波。我们发现，通过对粒子流密度$\langle j^{x}\rangle$给出不同的源$a_x$，可以得到不同的超流态。基于$a_x$，可以很容易地得到椭圆余弦波的三种极限情况以及椭圆余弦波的一般解。计算了这些超流态的化学势$μ$和粒子流密度$\langle j^x \rangle$，作为源$a_x$的函数，并与均匀超流进行了比较。我们发现随着$a_x$的增加，椭圆余弦波将进入均匀极限，这反映在椭圆余弦波和均匀超流之间的$μ(a_x)$和$\langle j^x(a_x) \rangle$的行为的汇合。基于准简正模，我们证明了由于有限的温度，弦波总是动力学不稳定的，而能量稳定性受粒子流密度的影响。这些证据表明，在有限温度超流系统中，椭圆余弦波可以看作是一个具有超固体性的\textcolor{black}{unstable excited states}。
英文摘要：
The candidate of supersolid-like state, cnoidal wave, is investigated in finite temperature holographic superfluid model for the first time. We find by giving different source $a_x$ for the particle current density $\langle j^{x}\rangle$, different kinds of superflow states can be obtained numerically. And based on $a_x$, three limiting cases of cnoidal waves can be found easily as well as the general cnoidal wave solution. The chemical potential $μ$ and particle current density $\langle j^x \rangle$, as functions of source $a_x$, are calculated for these superflow states and are compared with homogeneous superflow. We find as we increasing $a_x$, cnoidal waves will enter into the uniform limit, which reflects in the confluence of the behavior of $μ(a_x)$ and $\langle j^x(a_x) \rangle$ between cnoidal wave and homogeneous superflow. Based on the quasi-normal modes, we show the cnodial waves are always dynamically unstable due to the finite temperature, while the energetic stability is influenced by the particle current density. All these evidences manifest that the cnoidal wave can be seen as an \textcolor{black}{unstable excited states} with supersolidity in finite temperature superfluid system.
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