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Towards the thermodynamics of localization processes

Grigolini1, Pala, Palatella

  • 1Istituto 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.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

This study explores entropy in quantum models for Anderson localization. Using Tsallis entropy with index q=1/2 accelerates the emergence of the Kolmogorov regime, suggesting a signature for Anderson localization.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Anderson localization is a key phenomenon in disordered systems.
  • Entropy evolution in quantum systems exhibits distinct dynamic, thermodynamic, and saturation regimes.
  • Previous work identified three entropy regimes: transient, linear-in-time (Kolmogorov), and saturation.

Purpose of the Study:

  • To investigate the effect of nonextensive entropy on the time evolution of entropy in a quantum model for Anderson localization.
  • To compare the impact of Tsallis entropic index q=1/2 versus the traditional q=1.
  • To identify potential signatures of Anderson localization using entropic indicators.

Main Methods:

  • Utilized a quantum mechanical model, a prototype for Anderson localization.

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  • Employed Tsallis's nonextensive entropic indicator with a variable entropic index q.
  • Analyzed entropy time evolution across different regimes.
  • Adopted a two-site model for analytical treatment.

    • Main Results:

    • The adoption of the Tsallis entropic index q=1/2, compared to q=1, reduces the transient regime duration.
    • The q=1/2 index facilitates an earlier emergence of the Kolmogorov (linear-in-time) entropy regime.
    • Analytical treatment using a two-site model explains these observed properties.

    Conclusions:

    • The value q=1/2 for Tsallis entropy appears to accelerate the transition to thermodynamic behavior in this quantum model.
    • An earlier emergence of the Kolmogorov regime under q=1/2 may serve as a characteristic signature of Anderson localization.
    • This finding offers a novel perspective on characterizing localization phenomena through entropic dynamics.