论文标题
部分可观测时空混沌系统的无模型预测
Theory of proximity effect in $s+p$-wave superconductor junctions
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We derive a boundary condition for the Nambu Keldysh Green's function in diffusive normal metal / unconventional superconductor junctions applicable for mixed parity pairing. Applying this theory to a 1d model of $s+p$-wave superconductor, we calculate LDOS in DN and charge conductance of DN / $s+p$-wave superconductor junctions. When the $s$-wave component of the pair potential is dominant, LDOS has a gap like structure at zero energy and the dominant pairing in DN is even-frequency spin-singlet $s$-wave. On the other hand, when the $p$-wave component is dominant, the resulting LDOS has a zero energy peak and the dominant pairing in DN is odd-frequency spin-triplet $s$-wave. We show the robustness of the quantization of the conductance when the magnitude of $p$-wave component of the pair potential is larger than that of $s$-wave one. These results show the robustness of the anomalous proximity effect specific to spin-triplet superconductor junctions.
