Deformed Gaussian orthogonal ensemble and the statistical fluctuations in the spectra of the quartic oscillator

Abstract

The nearest-neighbor spacing distributions proposed by four models, namely, the Berry-Robnik, Caurier-Grammaticos-Ramani, Lenz-Haake, and the deformed Gaussian orthogonal ensemble, as well as the ansatz by Brody, are applied to the transition between chaos and order that occurs in the isotropic quartic oscillator. The advantages and disadvantages of these five descriptions are discussed. In addition, the results of a simple extension of the expression for the Dyson-Mehta statistic ${\ensuremath{\Delta}}_{3}$ are compared with those of a more popular one, usually associated with the Berry-Robnik formalism.