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arXiv 1405.7589cond-mat.other
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超流$^4$ He中涡旋的量子Monte Carlo研究及固体中涡旋态的寻找

Quantum Monte Carlo study of a vortex in superfluid $^4$He and search for a vortex state in the solid

Davide E. Galli, Luciano Reatto, Maurizio Rossi

摘要:

本文用阴影路径积分基态方法和固定相位近似对零温下凝聚态$^4$ He中的三维直量子化涡旋线进行了微观研究。我们的特点是能量和局部密度分布的涡轴周围的超流$^4$ He在几个密度,从低于平衡密度到过压制度。对于Onsager-Feynman(OF)阶段,我们的结果是准确的,并代表了其他理论的基准。在相位的回流相关性的列入改善了描述的涡相对于OF相位的拓扑激发的核心能量的大幅度减少。在所有密度下,回流相引起涡核的部分填充,并且这种填充随密度略有增加。随着密度的增加,核的尺寸略有减小,密度分布具有明确的密度相关振荡,其波矢量更接近于静态密度响应函数中的主峰波矢量,而不是圆波矢量。我们的结果可以应用于大半径$R$的涡环,我们发现很好的协议与实验值的能量作为$R$的函数没有任何自由参数。我们还研究了$^4$他以上的熔融密度在固相中使用相同的功能形式的相作为在液体中。我们发现,非对角属性的固体不定性的涡流相位引起的速度场的影响,无论有和没有回流相关。因此,我们发现的证据表明,一个完美的$^4$ He晶体是不是一个边缘稳定的量子固体中的旋转将能够诱导非对角的长程相干。

英文摘要:

We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed $^4$He at zero temperature using the Shadow Path Integral Ground State method and the fixed-phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid $^4$He at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius $R$ and we find good agreement with the experimental value of the energy as function of $R$ without any free parameter. We have studied also $^4$He above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect $^4$He crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.

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