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Are the phases in the Anderson model long-range correlated?

Author

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  • Kantelhardt, Jan W.
  • Berkovits, Richard
  • Havlin, Shlomo
  • Bunde, Armin

Abstract

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range correlated, decaying as a power law with time. It seems that the exponent depends on the degree of disorder. In d=3, close to the critical disorder wc=16.5, the correlation exponent exhibits a maximum value of α≈0.6 which is significantly above random fluctuations (α=0.5).

Suggested Citation

  • Kantelhardt, Jan W. & Berkovits, Richard & Havlin, Shlomo & Bunde, Armin, 1999. "Are the phases in the Anderson model long-range correlated?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 461-464.
    • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:461-464
    DOI: 10.1016/S0378-4371(98)00631-1
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    Cited by:

    1. Maria Pia Beccar Varela & Francis Biney & Ionut Florescu, 2015. "Long correlations and fractional difference analysis applied to the study of memory effects in high-frequency (tick) data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1365-1374, August.
    2. Mariani, M.C. & Florescu, I. & Beccar Varela, M.P. & Ncheuguim, E., 2010. "Study of memory effects in international market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1653-1664.
    3. Mariani, M.C. & Libbin, J.D. & Kumar Mani, V. & Beccar Varela, M.P. & Erickson, C.A. & Valles-Rosales, D.J., 2008. "Long correlations and Normalized Truncated Levy Models applied to the study of Indian Market Indices in comparison with other emerging markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1273-1282.

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