论文标题
部分可观测时空混沌系统的无模型预测
A quantum phase transition in the one-dimensional water chain
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。
The concept of quantum phase transitions (QPT) plays a central role in the description of condensed matter systems. In this contribution, we perform high-quality wavefunction-based simulations to demonstrate the existence of a quantum phase transition in a crucially relevant molecular system, namely water, forming linear chains of rotating molecules. We determine various critical exponents and reveal the water chain QPT to belong to the (1+1) dimensional Ising universality class. Furthermore, the effect of breaking symmetries is examined and it is shown that by breaking the inversion symmetry, the ground state degeneracy of the ordered quantum phase is lifted to yield two many-body states with opposite polarization. The possibility of forming ferroelectric phases together with a thermal stability of the quantum critical regime up to ~10 K makes the linear water chain a promising candidate as a platform for quantum devices.
