Bose-Einstein Condensation in the Framework of $\kappa$-Statistics

Abstract

In the present work we study the main physical properties of a gas of $\kappa$-deformed bosons described through the statistical distribution function $f_{\kappa }=Z^{-1}[{\exp }_{\kappa }(\beta (1/2m{v}^2-\mu ))-1{]}^{-1}$. The deformed $\kappa$-exponential ${\exp }_{\kappa }(x)$, recently proposed in Ref. [G.Kaniadakis, Physica A {\bf 296}, 405, (2001)], reduces to the standard exponential as the deformation parameter $\kappa \to 0$, so that $f_0$ reproduces the Bose-Einstein distribution. The condensation temperature $T_c^{\kappa }$ of this gas decreases with increasing $\kappa$ value, and approaches the ${}^{4}He(I){-}^{4}He(II)$ transition temperature $T_{\lambda }=2.17K$, improving the result obtained in the standard case ($\kappa =0$). The heat capacity $C_V^{\kappa }(T)$ is a continuous function and behaves as $B_{\kappa }{T}^{3/2}$ for $T<T_c^{\kappa }$, while for $T>T_c^{\kappa }$, in contrast with the standard case $\kappa =0$, it is always increasing. Pacs: 05.30.Jp, 05.70.-a Keywords: Generalized entropy; Boson gas; Phase transition.

To appear in Physica B. Two fig.ps

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