Abstract
In this paper the nearest-neighbor level-spacing distributions P(s) of the two-dimensional harmonic oscillator for which the energy contours are flat in the action space are calculated. It is found that P(s) for a given level group on an energy contour is not peaked about a nonzero value of s regardless of whether the oscillator frequency ratios are irrational or rational. The precise form of P(s) is a \ensuremath{\delta} function independent of the arithmetic nature of the frequency ratios. We propose another method of constructing P(s) in which many sets of levels are taken as a whole. Using this method, some surprising distributions, such as Gaussian orthogonal ensemble-like, Poisson-like, and unit-step-function-like distributions, are exhibited for some sets of levels far away from the scaled energy contours of the harmonic oscillator.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical review. A, Atomic, molecular, and optical physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
