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Fractional Statistics in terms of the r-Generalized Fibonacci Sequences

M. Rachidi·E. H. Saidi·J. Zerouaoui
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Abstract

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 $0\leq s\leq 1:mod(1)$. For quantum gases of quasiparticles with $s=1/M:mod(1)$, $M\geq 2,$, we show that the statistical weights densities $ρ_M$ 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.

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M. Rachidi, E. H. Saidi, J. Zerouaoui. 2001-09-07. Fractional Statistics in terms of the r-Generalized Fibonacci Sequences. https://doi.org/10.1142/s0217751x03012394

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