Comment on "Models of intermediate spectral statistics".
In this Comment we point out that the semi-Poisson is well suited only as a reference point for the so-called "intermediate statistics," which cannot be interpreted as a universal ensemble, like the Gaussian orthogonal ensemble or the Poissonian statistics. In Ref. 2 it was proposed that the nearest-neighbor distribution P(s) of the spectrum of a Poissonian distributed matrix perturbed by a rank one matrix is similar to the semi-Poisson distribution. We show, however, that the P(s) of this model differs considerably in many aspects from the semi-Poisson. In addition, we give an asymptotic formula for P(s) as s-->0, which gives P'(0)=pisqrt[3]/2 for the slope at s=0. This is different not only from the GOE case, but also from the semi-Poisson prediction.
Gorin
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Centro de Ciencias Físicas, Universidad Nacional Autónoma de México, Campus Morelos, Apartado Postal 48-3, Codigo Postal 62251, Cuernavaca, Morelos, Mexico.
Müller
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Seba
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