A one-dimensional Bose-Einstein condensate may experience nonlinear periodic modulations known as cnoidal waves. We argue that such structures represent promising candidates for the study of supersolidity-related phenomena in a nonequilibrium state. A mean-field treatment makes it possible to rederive Leggett's formula for the superfluid fraction of the system and to estimate it analytically. We determine the excitation spectrum, for which we obtain analytical results in the two opposite limiting cases of (i) a linearly modulated background and (ii) a train of dark solitons. The presence of two Goldstone (gapless) modes, associated with the spontaneous breaking of $\mathrm{U}\left(1\right)$ symmetry and of continuous translational invariance, at long wavelength is verified. We also calculate the static structure factor and the compressibility of cnoidal waves, which show a divergent behavior at the edges of each Brillouin zone.

中文翻译：

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超冷Bose气体中的虹膜波超固体

一维Bose-Einstein凝结物可能会经历非线性周期性调制，称为长波。我们认为，这样的结构代表了在非平衡状态下研究超固态相关现象的有希望的候选者。平均场处理使得可以为系统的超流体分数重新计算Leggett公式，并进行分析估计。我们确定了激发光谱，为此我们在（i）线性调制背景和（ii）一列暗孤子的两个相反的极限情况下获得了分析结果。两种金石（无间隙）模式的存在，与自发的$\mathrm{ü}（\mathrm{1个}）$验证了在长波长下的对称性和连续平移不变性。我们还计算了静态结构因子和正弦波的可压缩性，它们在每个布里渊区的边缘显示出不同的行为。