Abstract
We study by means of a kinetic approach recently proposed [Phys. Rev. E 49, 5103 (1994)] both classical and quantum statistics, stationary solutions of a non-linear Fokker-Planck equation. The non-linear term in this equation has origin in a generalized exclusion-inclusion principle which takes into account the quantum effects due to the bosonic, fermionic or intermediate behaviour of the particles. If the drift and diffusion coefficients are polynomials, in the velocity variable, of degree 2 M + 1 and 2 N, respectively, only one well-defined statistics can be derived, for any particular pair of values ( M, N). In the case of classical particles, in addition to the macroscopic Fokker-Planck equation, we derive the associated microscopic Langevin equation and demonstrate that the pairs (0,0), (1,0) and (0,1) correspond, respectively, to Maxwell-Boltzmann, Druyvenstein and Tsallis statistical distributions. We study also the distribution related to the pair (1, 1) which is the simplest generalization of the Tsallis [1] one. Finally, the above statistics are extended to the quantum case of particles obeying the exclusion-inclusion principle.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.