Abstract
The number of levels with energy less than E of an integrable quantum system with two degrees of freedom is equal to λE+, where λ is a constant and s a fluctuating quantity with a non-Gaussian distribution. The probability distribution of s decreases roughly like exp(-) when s is large. The number of levels between E and E+z √E is equal to λz √E + where r is another fluctuating quantity. The distribution of r tends to a Gaussian distribution as z→0 and oscillates around some limiting non-Gaussian distribution as z→∞.
- Received 30 August 1993
DOI:https://doi.org/10.1103/PhysRevLett.71.3047
©1993 American Physical Society