The energy level spacing for two harmonic oscillators with generic ratio of frequencies

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 ratio α no limit distribution exists, but for random α with any absolutely continuous distribution p(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. © 1991 Plenum Publishing Corporation.