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One dimensional localization for arbitrary disorder correlations

Author

Listed:
  • Hichem Eleuch

    (Institute for Quantum Science and Engineering, Texas A&M University
    College of Arts and Sciences, Abu Dhabi University)

  • Michael Hilke

    (McGill University
    Center for the Physics of Materials (CPM), McGill University)

Abstract

We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation and calculate all the correlators needed for the localization length expression. We compare our results with numerical results for the special case, where the autocorrelation decays quadratically with distance. We look at disorder ranging from weak to strong disorder, which shows excellent agreement. For the numerical simulation, we introduce a generic method to obtain a random potential with an arbitrary autocorrelation function. The correlated potential is obtained in terms of the convolution between a Wiener stochastic potential and a function of the correlation. Graphical abstract

Suggested Citation

  • Hichem Eleuch & Michael Hilke, 2019. "One dimensional localization for arbitrary disorder correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(12), pages 1-7, December.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:12:d:10.1140_epjb_e2019-100474-5
    DOI: 10.1140/epjb/e2019-100474-5
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