On fluctuations and localization length for the Anderson model on a strip

Ilia Binder; Michael Goldstein; Mircea Voda

On fluctuations and localization length for the Anderson model on a strip

Mathematical Physics 2014-05-06 v2 math.MP Spectral Theory

Authors: Ilia Binder , Michael Goldstein , Mircea Voda

Abstract

We consider the Anderson model on a strip. Assuming that potentials have bounded density with considerable tails we get a lower bound for the fluctuations of the logarithm of the Green's function in a finite box. This implies an effective estimate by $\exp(CW^2)$ for the localization length of the Anderson model on the strip of width $W$ . The results are obtained, actually, for a more general model with a non-local operator in the vertical direction.

Keywords

Anderson model strip localization length fluctuations Green's function

Cite

@article{arxiv.1310.0514,
  title  = {On fluctuations and localization length for the Anderson model on a strip},
  author = {Ilia Binder and Michael Goldstein and Mircea Voda},
  journal= {arXiv preprint arXiv:1310.0514},
  year   = {2014}
}

Comments

20 pages; v2: fixed a number of typos and small mistakes, added to the introduction

On fluctuations and localization length for the Anderson model on a strip

Abstract

Keywords

Cite

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