论文标题
在量子场理论的不可整合模型中混乱的签名
Signatures of Chaos in Non-integrable Models of Quantum Field Theory
论文作者
论文摘要
我们研究（1+1）d量子场理论（QFT）模型中量子混乱的特征。我们的分析基于哈密顿截断的方法，这是一种用于构建低能量光谱和QFT的特征状态的数值方法，可以将其视为准确解决模型的扰动。我们专注于双正弦波顿，还研究了巨大的正弦 - 戈登和$ {ϕ^4} $模型，所有这些模型都是不可集成的，可以通过这种方法研究以足够高的精度从小到中间扰动强度进行高精度。我们分析了水平间距和特征向量成分的统计数据，这两者均应遵循随机矩阵理论预测。相反，虽然水平间距统计数据接近高斯正交集合，但相反，特征向量成分遵循的分布与预期的高斯明显不同。与典型的量子混乱情况不同，水平间隔统计量向混乱行为的过渡已经发生在扰动状态下。另一方面，即使对于相对较大的扰动，特征向量组件的分布似乎也不会改变或接近高斯行为。此外，我们的结果表明这些功能独立于模型和基础的选择。
We study signatures of quantum chaos in (1+1)D Quantum Field Theory (QFT) models. Our analysis is based on the method of Hamiltonian truncation, a numerical approach for the construction of low-energy spectra and eigenstates of QFTs that can be considered as perturbations of exactly solvable models. We focus on the double sine-Gordon, also studying the massive sine-Gordon and ${ϕ^4}$ model, all of which are non-integrable and can be studied by this method with sufficiently high precision from small to intermediate perturbation strength. We analyze the statistics of level spacings and of eigenvector components, both of which are expected to follow Random Matrix Theory predictions. While level spacing statistics are close to the Gaussian Orthogonal Ensemble as expected, on the contrary, the eigenvector components follow a distribution markedly different from the expected Gaussian. Unlike in the typical quantum chaos scenario, the transition of level spacing statistics to chaotic behaviour takes place already in the perturbative regime. On the other hand, the distribution of eigenvector components does not appear to change or approach Gaussian behaviour, even for relatively large perturbations. Moreover, our results suggest that these features are independent of the choice of model and basis.
