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首页> 外文期刊>Journal of Statistical Physics >Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions
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Exact and Asymptotic Features of the Edge Density Profile for the One Component Plasma in Two Dimensions

机译：一维等离子体在二维中的边缘密度轮廓的精确和渐近特征

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There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires continuation beyond the finite geometry used in its derivation. We consider both disk and cylinder geometry, and focus attention on the exact and asymptotic features of the edge density. At the special coupling the system is exactly solvable. In particular the -point correlation can be written as a determinant, allowing the edge density to be computed to first order in . A double layer structure is found, which in turn implies an overshoot of the density as the edge of the leading support is approached from the interior. Asymptotic analysis shows that the deviation from the leading order (step function) value is different for the interior and exterior directions. For general , a Gaussian fluctuation formula is used to study the large deviation form of the density for large but finite. This asymptotic form involves thermodynamic quantities which we independently study, and moreover an appropriate scaling gives the asymptotic decay of the limiting edge density outside of the plasma.
机译：对于分数量子霍尔效应，在劳克林试验波函数与二维单组分等离子体的玻耳兹曼因子之间存在众所周知的类比。后者需要超越其推导中使用的有限几何形状的延续。我们同时考虑了圆盘和圆柱的几何形状，并将注意力集中在边缘密度的精确和渐近特征上。在特殊的联轴器上，系统是完全可解决的。特别地，可以将点相关性写为行列式，从而允许将边沿密度计算为中的一阶。发现了双层结构，这又意味着当从内部接近前导支架的边缘时，密度过高。渐近分析表明，内部和外部方向与领先顺序（阶跃函数）值的偏差不同。通常，使用高斯涨落公式来研究大而有限的密度的大偏差形式。这种渐近形式涉及我们独立研究的热力学量，此外，适当的缩放比例可提供等离子外部极限边沿密度的渐近衰减。

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