Summary
The so-called «Legendre» ensemble of random matrices is studied for the nontrivial cases β=1 and 4. As for the more trivial case β=2 the level density has a behaviour in qualitative agreement with nuclear and atomic densities,i.e. it is concave upward and rises rapidly. The nearest-neighbour spacing distributions are obtained for β=1,4; they are the same as for the Gaussian and circular ensembles.
Riassunto
Si studia il cosiddetto insieme «di Legendre» di matrici casuali nei casi non banali β=1 e 4. Come nel più banale caso β=2 la densità dei livelli ha comportamento che concorda qualitativamente con le densità atomiche e nucleari, cioè è concava verso l’alto e sale rapidamente. Si ottengono le distribuzioni delle spaziature dei prossimi vicini per β=1,4; esse sono uguali a quelle degli insiemi gaussiani e circolari.
Резюме
Для нетривиальных сличаев β=1 и 4 исследуется так называемый ансамбль «Лежандра» случайных матриц. Как для более тривиального случая β=2, плотность уровней имеет поведение, которое качественно согласуется с ядерными и атомными плотностями, т.е. является вогнутой кверху и быстро возрастает. Для β=1, 4 получаются распределения расстояний мезду ближайшами соседями. Распределения являются такими же, как и в случае гауссова и кольцевого ансамблей.
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Supported by the Ministère de l’Education du Gouvernement de Québec.
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Vo-Dai, T., Derome, J.R. Correlation between eigenvalues of random matrices. Nuov Cim B 30, 239–253 (1975). https://doi.org/10.1007/BF02725699
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DOI: https://doi.org/10.1007/BF02725699