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Condensed Matter > Statistical Mechanics

arXiv:1503.06010 (cond-mat)
[Submitted on 20 Mar 2015 (v1), last revised 20 Aug 2015 (this version, v2)]

Title:A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data

Authors:Minoru Biyajima, Takuya Mizoguchi, Naomichi Suzuki
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Abstract:By applying fractional calculus to the equation proposed by M. Planck in 1900, we obtain a new blackbody radiation law described by a Mittag-Leffler (ML) function. We have analyzed NASA COBE data by means of a non-extensive formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a fractional parameter $(\alpha-1)$, and our new formula including a parameter $(p-1)$, as well as the Bose-Einstein distribution with a dimensionless chemical potential $\mu$. It can be said that one role of the fractional parameter $(p-1)$ is almost the same as that of chemical potential $(\mu)$ as well as that of the parameter $(q-1)$ in the non-extensive approach.
Subjects: Statistical Mechanics (cond-mat.stat-mech); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1503.06010 [cond-mat.stat-mech]
  (or arXiv:1503.06010v2 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.1503.06010
Related DOI: https://doi.org/10.1016/j.physa.2015.08.015

Submission history

From: Takuya Mizoguchi [view email]
[v1] Fri, 20 Mar 2015 07:28:24 UTC (19 KB)
[v2] Thu, 20 Aug 2015 04:44:55 UTC (85 KB)
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