Fractional Statistics in terms of the r-Generalized Fibonacci Sequences
نویسنده
چکیده
We develop the basis of the two dimensional generalized quantum statistical systems by using results on r-generalized Fibonacci sequences. According to the spin value s of the 2d-quasiparticles, we distinguish four classes of quantum statistical systems indexed by s = 0, 1/2 : mod(1), s = 1/M : mod(1), s = n/M : mod(1) and 0 ≤ s ≤ 1 : mod(1). For quantum gases of quasiparticles with s = 1/M : mod(1), M ≥ 2,, we show that the statistical weights densities ρM are given by the integer hierarchies of Fibonacci sequences. This is a remarkable result which envelopes naturally the Fermi and Bose statistics and may be thought of as an alternative way to the Haldane interpolating statistical method. PACS number: 05.30.-d/11.10.-z/11.30.Ly. 2000 MSC : 40A05, 40A25 Département de Mathématiques et Informatique, Faculté des Sciences de Rabat, B.P. 1014, Rabat, Morocco. Laboratoire de Physique Théorique et Appliquée LPTA, Faculté des Sciences de Kénitra, Morocco
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