Fractional Statistics in terms of the r-Generalized Fibonacci Sequences

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 $0\le s\le 1:mod(1)$. For quantum gases of quasiparticles with $s=1/M:mod(1)$, $M\ge 2,$, we show that the statistical weights densities ${\rho }_M$ 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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References in corpus (1)

• Non Trivial Extension of the (1+2)-Poincaré Algebra and Conformal Invariance on the Boundary of $Ad{S}_3$

Cited by in corpus (1)

• Generalized Heisenberg algebras and k-generalized Fibonacci numbers