Towards the Thermodynamics of Localization Processes

TL;DR

This paper investigates the entropy evolution in a quantum model related to Anderson localization, demonstrating that a non-extensive entropy with a specific parameter enhances the clarity of the thermodynamic regime, potentially indicating localization.

Contribution

It introduces the use of a non-extensive entropy with a mobile index to better characterize localization regimes in quantum models, providing analytical insights.

Findings

The non-extensive entropy with q=1/2 extends the thermodynamic regime.

The q=1/2 entropy makes the localization regime more distinct.

Analytical model supports the significance of q=1/2 in localization detection.

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 [V. Latora, M. 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, namely a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that with the adoption of the ``magic'' value q = Q = 1/2 the Kolmogorov regime becomes more extended and more distinct than with the traditional entropic index q = 1. 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's localization.