Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

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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 Δ₃(L) do not follow Poisson statistics. In particular, P(s) shows a sharp peak at s=1 while Δ₃(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.