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Self-similarity among energy eigenstates.

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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… Click to show full abstract

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.

Keywords: energy; self similarity; among energy; similarity among; energy eigenstates

Journal Title: Physical review. E
Year Published: 2022

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