Blackbody Radiation in $q$-deformed Statistics

Abstract

More general canonical ensemble which gives rise the generalized statistics or $q$-deformed statistics can represent the realistic scenario than the ideal one, with proper parameter sets involved. We study the Planck's law of blackbody radiation, Wein's and Rayleigh-Jeans radiation formulae from the point of view of $q$-deformed statistics. We find that the blackbody energy spectrum curve for a given temperature $T$ corresponding to different $q$ values differs from each other: the location of the peak(i.e. ${\nu }_m$) of the energy distribution $u_{\nu }$ (corresponding to different $q$ ) shifted towards higher $\nu$ for higher $q$. From the $q$-deformed Wein's displacement law, we find that ${\lambda }_{m}T$ varies from $0.0029\mathrm{m}\mathrm{K}$ to $0.0017\mathrm{m}\mathrm{K}$ as the deformation parameter $q$ varies from $1.0$(undeformed) to $1.1$(deformed).

13 Pages, 5 figures

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