- th / 0 10 40 33 v 2 1 8 D ec 2 00 6 LIMIT DISTRIBUTIONS OF MANY – PARTICLE SPECTRA AND q - DEFORMED GAUSSIAN VARIABLES
نویسنده
چکیده
We find the limit distributions for a spectrum of a system of n particles governed by a k–body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q–deformed Gaussian distribution with the deformation parameter q depending on the value of the fraction k √ n . The family of q–deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig67, Wig57], Mon and French [MF75]. PACS: 05.40.+j
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تاریخ انتشار 2006