q-Gaussians in the porous-medium equation: stability and
time evolution |
| |
Authors: | V Schwämmle F D Nobre C Tsallis |
| |
Institution: | (1) Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180, Brazil;(2) Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA |
| |
Abstract: | The stability of q-Gaussian distributions as particular solutions of the
linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical
and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index qi, approaches asymptotically the
final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for
the kurtosis evolves in time according to a q-exponential, with a relaxation index qrel ≡qrel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (qi ≥ 5/3) into a finite-variance
one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light
on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary
states to the ultimate thermal equilibrium
state. |
| |
Keywords: | PACS" target="_blank">PACS 05 40 Fb Random walks and Levy flights 05 20 -y Classical statistical mechanics 05 40 Jc Brownian motion |
本文献已被 SpringerLink 等数据库收录! |
|