International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
Phys Rev E. 2023 Mar;107(3-1):034123. doi: 10.1103/PhysRevE.107.034123.
In a quantum system, different energy eigenstates have different properties or features, allowing us to define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstate in an energy shell [E_{c}-ΔE/2,E_{c}+ΔE/2] is invariant with changing width ΔE or Planck constant ℏ 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.
在量子系统中，不同的能量本征态具有不同的性质或特征，这使得我们可以定义一个分类器将它们分为不同的组。我们发现，只要壳层中的本征态数量足够大，在能量壳层[E_{c}-ΔE/2，E_{c}+ΔE/2]中每种能量本征态的比例与改变宽度ΔE或普朗克常数ℏ无关。我们给出了一个论点，即这种能量本征态的自相似性是所有量子系统的一个普遍特征，并通过各种量子系统，包括圆形 billiard、双尖模型、踢转子和海森堡 XXZ 模型进行了数值说明。
