Polynomial expansion of diffusion and drift coefficients for classical and quantum statistics

G. Kaniadakis and P. Quarati

Physica A: Statistical Mechanics and its Applications, 1997, vol. 237, issue 1, 229-239

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 2M + 1 and 2N, 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.

Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437196003780
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:237:y:1997:i:1:p:229-239

DOI: 10.1016/S0378-4371(96)00378-0

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().