论文标题
能量特征状态之间的自相似性
Self-Similarity Among Energy Eigenstates
论文作者
论文摘要
在量子系统中，不同的能量本征具有不同的特性或特征，使我们定义了分类器将它们分为不同的组。我们发现能量外壳$ [e_ {c}-Δe/2，e_ {c}+Δe/2] $的每种类型的能量本质状态的比率是不变的，而更改宽度$ΔE$或planck常数$ \ hbar $，只要壳中的本特征数量就足够大。我们提出了一个论点，即能量本征态中这种自相似性是所有量子系统的一般特征，它通过各种量子系统（包括圆形台球，双顶模型，踢rodor和Heisenberg XXZ模型）进一步说明，该系统可以进一步说明。
In a quantum system, different energy eigenstates have different properties or features, allowing us define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstates in an energy shell $[E_{c}-ΔE/2,E_{c}+ΔE/2]$ is invariant with changing width $ΔE$ or Planck constant $\hbar$ as long as the number of eigenstates in the shell is statistically large enough. We give an argument that such self-similarity in energy eigenstates is a general feature for all quantum systems, which is further illustrated numerically with various quantum systems, including circular billiard, double top model, kicked rotor, and Heisenberg XXZ model.
