Limit distributions of many-particle spectra

Details Limit distributions of many-particle spectra Limit distributions of many-particle spectra

2001-04-10

arxiv.org/abs/nucl-th/0104033v2

Quantum probability, 409--414, Banach Center Publ., 73, Polish Acad. Sci., Warsaw, 2006

Physics

Nuclear Physics

Nuclear Theory

8 pages, 6 figures

Scientific paper

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 \frac{k}{\sqrt{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, Mon and French.

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