Summary
We use a generalisation of a formula introduced by Mehta to analyse the dependence of the spacing distribution on the region of the spectrum. Such a dependence, which usually receives little attention, is however an important feature of the statistics of spacings. Our examples are physical systems constituted of the sum of non-interacting subsystems whose spacing distributions obey the Poisson law; we have found that the spacing distributions of the total systems are quite complicated, even if their histograms may look approximately like exponentials. The formulae we have obtained for the local spacing distributions and for the means of such distributions have been tested by means of numerical simulations obtaining a satisfactory consistence.
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Work partially supported by INFN and INFM.
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Mezzadri, F., Scotti, A. On the locality of level spacing distributions. Nuov Cim B 111, 615–622 (1996). https://doi.org/10.1007/BF02726653
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DOI: https://doi.org/10.1007/BF02726653