Towards the thermodynamics of localization processes

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 the...

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Published in:Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000-09, Vol.62 (3 Pt A), p.3429-3436
Main Authors: Grigolini, P, Pala, MG, Palatella, L, Roncaglia, R
Format: Article
Language:English
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Summary: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.
ISSN:1063-651X
1095-3787
DOI:10.1103/PhysRevE.62.3429