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arXiv · 2209.11256

Self-Similarity Among Energy Eigenstates

Zhelun Zhang·Zhenduo Wang·Biao Wu
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Abstract

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 $[E_{c}-\Delta E/2,E_{c}+\Delta E/2]$ is invariant with changing width $\Delta E$ 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.

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Zhelun Zhang, Zhenduo Wang, Biao Wu. 2022-09-22. Self-Similarity Among Energy Eigenstates. https://doi.org/10.1103/physreve.107.034123

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