Classical model of intermediate statistics
- Dipartimento di Fisica, Istituto Nazionale di Fisica Nucleare, Istituto Nazionale di Fisica della Materia, Politecnico di Torino, 10129 Torino (Italy)
In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials [eta][sub [kappa][kappa][prime]]. 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 fermion mixing in a [ital D]-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential [eta][sub BF]. This family contains, as a particular case when [eta][sub BF]=0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature [ital T][r arrow][infinity], the system is composed by an equal number of bosons and fermions, regardless of the value of [eta][sub BF]. On the contrary, when [ital T]=0, [eta][sub BF] becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions.
- OSTI ID:
- 7112697
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 49:6; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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