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The energy level spacing for two harmonic oscillators with generic ratio of frequencies |
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| Authors: | P M Bleher |
| Institution: | (1) Department of Mathematics, Hill Center, Busch Campus, Rutgers University, 08903 New Brunswick, New Jersey;(2) School of Mathematical Sciences, Tel-Aviv University, 69978 Ramat-Aviv, Israel |
| 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 no limit distribution exists, but for random with any absolutely continuous distributionp()d on 0, 1] a universal random limit distribution of the energy level spacing exists. Some properties of the random limit distribution are discussed. |
| Keywords: | Two-dimensional quantum harmonic oscillator distribution of energy level spacing continued fractions the Gauss map natural extension of invariant measures universality and rigidity of the spectrum |
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