论文标题
部分可观测时空混沌系统的无模型预测
Operational regimes of lasers based on gain media with a large Raman scattering cross-section
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 report on unusual regimes of operation of a laser with a gain medium with a large Raman scattering cross-section, which is often inherent in new types of gain media such as colloidal and epitaxial quantum dots and perovskite materials. These media are characterized by a strong electron-phonon coupling. Using the Fröhlich Hamiltonian to describe the electron-phonon coupling in such media, we analyze the operation of the system above the lasing threshold. We show that below a critical value of the Fröhlich constant, the laser can only operate in the conventional regime: namely, there are coherent cavity photons but no coherent phonons. Above the critical value, a new pump rate threshold appears. Above this threshold, either joint self-oscillations of coherent phonons in the gain medium and photons in a cavity or a chaotic regime are established. We also find a range of the values of the Fröhlich constant, the pump rate, and the resonator eigenfrequency, in which more than one dynamical regime of the system is stable. In this case the laser dynamics is determined by the initial values of the resonator field, the active medium polarization, the population inversion, and phonon amplitude.