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Paper   IPM / Physic / 11304
School of Physics
  Title:   Irrational Anomalies in One-Dimensional Anderson Localization
  Author(s):  R. Sepehrinia
  Status:   Published
  Journal: Phys. Rev. B
  Vol.:  82
  Year:  2010
  Pages:   045118
  Supported by:  IPM
  Abstract:
Lyapunov exponent (LE) of Anderson model with additional hopping term to the second nearest neighbor, is analyzed within the second order perturbation expansion in strength of diagonal disorder. Depending on hopping integrals, there are two propagating channels in a range of energies. By comparison with exact numerical results, we show that naive perturbation theory fails to give accurate Lyapunov exponents at such energies. New anomalies of Kappus-Wegner type emerge when hopping to second neighbor is allowed which are non-universal in the sense that is described below. It is shown that suitable averages in the first order of perturbation theory, develop singularities at these anomalous energies which enable us to locate them.


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