CLASSICAL-MODEL OF INTERMEDIATE STATISTICS

In this work we present a classical kinetic model of intermediate stat istics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as th e Maxwell-Boltzmann (MB) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-i nclusion principle. In our model the intermediate statistics are obtai ned as steady states of a system of coupled nonlinear kinetic equation s, where the coupling constants are the transmutational potentials eta (kappakappa'). We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fer mion mixing in a D-dimensional space, we obtain a family of FD-BE inte rmediate statistics by varying the transmutational potential eta(BF). This family contains, as a particular case, when eta(BF) = 0, the quan tum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Le tt. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE sta tistics, we derive an analytic expression of the fraction of fermions. When the temperature T --> infinity, the system is composed by an equ al number of bosons and fermions, regardless of the value of eta(BF). On the contrary, when T --> 0, eta(BF) becomes important and, accordin g to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions.