Single parameter scaling in one-dimensional localization revisited

Details Single parameter scaling in one-dimensional localization revisited Single parameter scaling in one-dimensional localization revisited

1999-09-10

arxiv.org/abs/cond-mat/9909155v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

Phys. Rev. Lett. 84, 2678 (2000)

Scientific paper

10.1103/PhysRevLett.84.2678

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $\delta$-functions with random strength.

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