二次“微笑”带隙介观涨落的普适性质
Universal Properties of Mesoscopic Fluctuations of the Secondary "Smile" Gap
摘要：
在介观系统中，准连续谱的能级在位置上波动，波动的分布揭示了所考虑结构的微观性质的信息。在这里，我们调查介观波动的二次“微笑”的差距，出现在准经典频谱的混沌腔耦合到一个或多个超导体。利用随机矩阵模型，我们数值计算了Andreev能级的能量和访问的间隙宽度的分布。我们主要集中在普适机制$E_{\mathrm{Th}}\ggΔ$，其中$E_{\mathrm{Th}}$是腔的无功能量，$Δ$是超导能隙。我们发现，该分布是由一个中间能级尺度$Δ_g$决定的，其值介于腔中的能级间距$δ_s$和带隙的准经典值$E_g$之间。从我们的数值，我们外推的前两个累积量的间隙分布在大的水平和通道数的限制。我们发现，在这个制度的规模分布是特雷西Widom分布：发现由Vavilov等人相同。\textbf{86}，874（2001）]，以获得相反极限$E_{\mathrm{Th}}\ll Δ$中的小间隙边缘的分布。这使我们得出这样的结论，发现的分布是一个普遍的性质的混沌邻近系统的边缘的连续谱。
英文摘要：
The energy levels of a quasi-continuous spectrum in mesoscopic systems fluctuate in positions, and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of the secondary "smile" gap, that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime $E_{\mathrm{Th}}\ggΔ$ with $E_{\mathrm{Th}}$ being the Thouless energy of the cavity and $Δ$ being the superconducting gap. We find that the distribution is determined by an intermediate energy scale $Δ_g$ with the value between the level spacing in the cavity $δ_s$ and the quasiclassical value of the gap $E_g$. From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov at al. [Phys. Rev. Lett. \textbf{86}, 874 (2001)] for the distribution of the minigap edge in the opposite limit $E_{\mathrm{Th}}\ll Δ$. This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum.
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