Comment on “Vortex distribution in a confining potential”

A system of interacting vortices is considered as an appropriate model for describing properties of type-II superconductors, and it has been shown lately to be deeply associated with nonextensive statistical mechanics. Herein we comment on a recent investigation of this model [M. Girotto, A. P. dos Santos, and Y. Levin, Phys. Rev. E 88, 032118 (2013)], which tried to contradict this assertion, based on a mean-field type of solution, compared with numerical-simulation data that correspond typically to a regime characterized by low concentrations of particles, as well as very high temperatures. It is shown that the physical situations analyzed differ significantly from those of a real superconducting phase. The analytical solution obtained from such a mean-field approximation shows a discrepancy with respect to the results of molecular-dynamics numerical simulations, which increases as the temperature is lowered towards the superconducting phase, as expected. We demonstrate that these results, when interpreted properly by means of an analytical solution within the framework of nonextensive statistical mechanics, present a remarkable agreement between molecular-dynamics simulations and theoretical results, for all temperatures, specially for those temperatures associated with the existence of type-II superconductivity.

Figure 1

Dimensionless stationary-state density profiles are presented versus $x/\lambda$ for different choices of $\epsilon$ and $\chi$ (precisely the same used in Fig. 3 of GSL [12]): (a) $\epsilon =0.49$ and $\chi =0.1225$; (b) $\epsilon =1$ and $\chi =0.25$; (c) $\epsilon =1.96$ and $\chi =0.49$; (d) $\epsilon =4$ and $\chi =1$. This sequence of parameters corresponds to a gradual decrease in the temperature from (a) to (d). The circles represent data from MD simulations, the full line represents the $W$-Lambert solution of Eq. (3), whereas the red dashed line corresponds to the mean-field approximation of GSL.