论文标题
部分可观测时空混沌系统的无模型预测
A construction of exotic metallic states
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 discuss examples of two dimensional metallic states with charge fractionalization, and we will demonstrate that the mechanism of charge fractionalization leads to exotic metallic behaviors at low and intermediate temperature. The simplest example of such state is constructed by fermionic partons at finite density coupled to a $Z_N$ gauge field, whose properties can be studied through rudimentary methods. This simple state has the following exotic features: (1) at low temperature this state is a "bad metal" whose resistivity can exceed the Mott-Ioffe-Regel limit; (2) while increasing temperature $T$ the resistivity $ρ(T)$ is a nonmonotonic function, and it crosses over from a bad metal at low $T$ to a good metal at relatively high $T$; (3) the optical conductivity $σ(ω)$ has a small Drude weight at low $T$, and a larger Drude weight at intermediate $T$; (4) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law. A more complex example with fermionic partons at finite density coupled to a SU(N) gauge field will also be constructed.