论文标题
部分可观测时空混沌系统的无模型预测
Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
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 use tensor network simulations to calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. We consider ground state quenches towards mesonic parameter ranges with confined fermion pairs as nonperturbative bound states in a semiclassical regime and the relativistic E$_8$ theory. We find that in both cases only the dominant eigenvalue of the modular Hamiltonian fully encodes the meson content of the quantum many-body system or quantum field theory, giving rise to nearly identical entanglement oscillations in the entanglement entropy. When the initial state is prepared in the paramagnetic phase, the return rate density exhibits regular cusps at unequally spaced positions, signaling the appearance of dynamical quantum phase transitions, at which the entanglement spectrum remains gapped. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent of systems in high-energy physics.
