title: Towards the thermodynamics of localization processes
abstract: We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [Phys. Rev. Lett. 82, 520 (1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis [J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that the adoption of the "magic" value q=Q=1/2, compared to the traditional entropic index q=1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q=1/2 might be a typical signature of the occurrence of Anderson localization.
authors.affiliation: Istituto di Biofisica CNR, Area della Ricerca di Pisa, Via Alfieri 1, San Cataldo 56010 Ghezzano-Pisa, Italy and Center for Nonlinear Science, University of North Texas, P.O. Box 5368, Denton, Texas 76203-5368 and Dipartimento di Fisica dell'Uni.
authors.initials: P
authors.lastname: Grigolini
authors.initials: MG
authors.lastname: Pala
authors.initials: L
authors.lastname: Palatella
authors.initials: R
authors.lastname: Roncaglia