论文标题
部分可观测时空混沌系统的无模型预测
Chaos due to symmetry-breaking in deformed Poisson ensemble
论文作者
论文摘要
在哈密顿量中，强度与耦合项之间的竞争定义了许多现象学模型，这些模型表现出光谱特性在Poisson（可集成）和Wigner-Dyson（混乱）合奏之间插值。重要的是要了解哈密顿式的偏离术语如何变化，因为一个或多个可集成系统的对称性被明确破坏。我们介绍了一个变形的泊松集合，以证明将耦合术语的精确映射到哈密顿的基础对称性上。根据最大熵原理，我们预测了一个混乱的极限，该限制可以从光谱特性和生存概率计算上进行数值验证。
The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal terms of a Hamiltonian evolve as one or more symmetries of an integrable system are explicitly broken. We introduce a deformed Poisson ensemble to demonstrate an exact mapping of the coupling terms to the underlying symmetries of a Hamiltonian. From the maximum entropy principle we predict a chaotic limit which is numerically verified from the spectral properties and the survival probability calculations.
