Abstract
The limit distribution of energy level spacing is studied for the system of two harmonic oscillators with generic ratio of frequencies. It is proved that for any fixed generic ratioα no limit distribution exists, but for randomα with any absolutely continuous distributionp(α)dα on [0, 1] a universal random limit distribution of the energy level spacing exists. Some properties of the random limit distribution are discussed.
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Bleher, P.M. The energy level spacing for two harmonic oscillators with generic ratio of frequencies. J Stat Phys 63, 261–283 (1991). https://doi.org/10.1007/BF01026603
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DOI: https://doi.org/10.1007/BF01026603