Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-09-27
Phys.Rev. E65 (2002) 016123
Physics
High Energy Physics
High Energy Physics - Phenomenology
10 pages, 8 figures, submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.65.016123
The Fokker-Planck equation is considered, which is connected to the birth and death process with immigration by the Poisson transform. The fractional derivative in time variable is introduced into the Fokker-Planck equation. From its solution (the probability density function), the generating function (GF) for the corresponding probability distribution is derived. We consider the case when the GF reduces to that of the negative binomial distribution (NBD), if the fractional derivative is replaced to the ordinary one. Formulas of the factorial moment and the $H_j$ moment are derived from the GF. The $H_j$ moment derived from the GF of the NBD decreases monotonously as the rank j increases. However, the $H_j$ moment derived in our approach oscillates, which is contrasted with the case of the NBD. Calculated $H_j$ moments are compared with those given from the data in $p\bar{p}$ collisions and in $e^+e^-$ collisions.
Biyajima Minoru
Suzuki Nao
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