E. Miraldi | Searcharxiv

arXiv2002

Cole-Hopf Like Transformation for a Class of Coupled Nonlinear Schroedinger Equations

In this paper we consider a class of coupled nonlinear Schroedinger equations for the fields $ψ_i$ containing complex nonlinearities, that has been obtained by requiring that the norms $|ψ_i|^2$ are conserved densities. For this class of equations we introduce a Cole-Hopf like transformation, whose effect is to reduce the complex nonlinearities into real ones, this way reducing the continuity equations of the system to the standard bilinear form. Some examples are presented to illustrate the applicability of the method. Pacs numbers: 03.50.-z, 03.65.-w, 11.30.Na, 11.40.Dw Keywords: Coupled nonlinear Schroedinger equations, Cole-Hopf transformation, Nonlinear transformations.

quant-ph↗

arXiv2002

Bose-Einstein Condensation in the Framework of $κ$-Statistics

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

cond-mat.stat-mech↗