Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

Details Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

2001-09-08

arxiv.org/abs/cond-mat/0109153v1

Phys. Rev. E 64, 066201 (2001)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.64.066201

The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $\Delta_3(L)$ do not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at $s=1$ while $\Delta_3(L)$ for small values of $L$ follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.

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