论文标题
部分可观测时空混沌系统的无模型预测
Energy transfer in quantum molecular chain -- two models of inhomogeneity
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 study a linear chain of oscillators with inhomogeneity in their interactions with phonon bath. In a previous work on the Markovian master equation of the system, we investigated a model in which the difference in the site-phonon coupling between adjacent oscillators is the same throughout the chain. Here we look into another model in which the oscillators are coupled to the phonon bath with alternating strength at successive sites. Whereas in the first model all exciton modes are connected, in the second model they are coupled in pairs that are not connected to each other. Owing to this special structure in the coupling, the excitation numbers of different modes can be solved exactly in the steady state. In the first model, the minima of the excitation profile in the site basis occur at the edges of the chain, whereas in the second model the maxima occur at the edges. The energy transfer efficiency in the first model is affected by the source power whereas in the second model the efficiency is independent of it. A distinct feature in the second model is that a sink placed at the middle of the chain is able to distinguish between chains with even and odd number of sites. The energy transfer efficiency in a chain with even number of sites is higher than a chain with odd number of sites. Therefore, it reveals the discrete nature of the chain. In the limit of very long chain when the discreteness of the chain is less evident, the efficiencies approach each other.
