论文标题
部分可观测时空混沌系统的无模型预测
Controlling Collective Phenomena by Engineering the Quantum State of Force Carriers: The Case of Photon-Mediated Superconductivity and its Criticality
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。
How are the scattering between the constituents of matter and the resulting collective phenomena affected by preparing the force carriers in different quantum states? This question has become experimentally relevant in a specific non-relativistic version of QED implemented within materials, where standard techniques of quantum optics are available for the preparation of desired quantum states of the carrier photon. We develop the necessary non-equilibrium approach for computing the vertex function and find that, in addition to the energy and momentum structure of the scattering, a further structure emerges which reflects the Hilbert-space distribution of the carrier quantum state. This emergent structure becomes non-trivial for non-Gaussian quantum states of the force carrier, and can dramatically affect interactions and collective phenomena. As a first application, we show that by preparing photons in pure Fock states one can enhance pair correlations, and even control the criticality and universality class of the superconducting phase transition by the choice of the number of photons. Our results also reveal that the thermal mixture of Fock states regularises the strong pair correlations present in each of its components, yielding the standard Bardeen-Cooper-Schrieffer criticality.
