标题： 无监督技术检测量子混沌 显示英文标题

标题： Unsupervised Techniques to Detect Quantum Chaos

摘要： 传统的量子混沌光谱探测需要量子哈密顿量的本征值，有时还需要本征向量。 这涉及计算成本高昂的对角化过程。 我们测试一种无监督神经网络是否可以直接从哈密顿量矩阵中检测量子混沌。 我们使用一个具有潜在随机图结构和随机耦合常数的单体哈密顿量，其中有一个参数决定了图的随机性。 光谱分析显示，增加潜在图中的随机性会导致从可积光谱统计到混沌光谱的转变。 我们表明，可以通过无监督神经网络，或者更具体地说，通过自组织映射，直接将哈密顿量矩阵输入神经网络来检测这种转变，而无需任何对角化过程。 显示英文摘要

摘要： Conventional spectral probes of quantum chaos require eigenvalues, and sometimes, eigenvectors of the quantum Hamiltonian. This involves computationally expensive diagonalization procedures. We test whether an unsupervised neural network can detect quantum chaos directly from the Hamiltonian matrix. We use a single-body Hamiltonian with an underlying random graph structure and random coupling constants, with a parameter that determines the randomness of the graph. The spectral analysis shows that increasing the amount of randomness in the underlying graph results in a transition from integrable spectral statistics to chaotic ones. We show that the same transition can be detected via unsupervised neural networks, or more specifically, Self-Organizing Maps by feeding the Hamiltonian matrix directly into the neural network, without any diagonalization procedure.