Enciso, AlbertoFinkel Morgenstern, FedericoGonzález López, Artemio2023-06-202023-06-202009-061539-375510.1103/PhysRevE.79.060105https://hdl.handle.net/20.500.14352/44675©2009 The American Physical Society. This work was supported in part by the MICINN and the UCM-Banco Santander under Grants No. FIS2008-00209 and No. GR58/08-910556. A.E. acknowledges the financial support of the Spanish Ministry of Science. The authors would also like to thank the referees for several useful remarks.We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.engjournal articlehttp://dx.doi.org/10.1103/PhysRevE.79.060105http://journals.aps.orgopen access51-73Física-Modelos matemáticosFísica matemática