论文标题
部分可观测时空混沌系统的无模型预测
Exact analytic formula for conductance predicting a tunable Sommerfeld-Arrhenius thermal transition within a single-step tunneling mechanism in molecular junctions subject to mechanical stretching
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 show that the conductance $G$ of molecular tunnel junctions wherein the charge transport is dominated by a single energy level can be expressed in closed analytic form which is exact and valid at arbitrary temperature $T$ and model parameter values. On this basis, we show that the single-step tunneling mechanism is compatible with a continuous thermal transition from a weakly $T$-dependent $G$ at low $T$ (Sommerfeld regime) to a nearly exponential $1/T$-dependent $G$ at high $T$ (Arrhenius-like regime). We predict that this Sommerfeld-Arrhenius transition can be observed in real molecular junctions % (e.g., based on perylene diimide) and can be continuously tuned, e.g., via mechanical stretching.
