On the role of the symmetry parameter $β$ in the strongly localized regime

Abstract

The generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the description of transport in strongly disordered systems replaces the symmetry parameter $β$ by a new parameter $γ$, which decreases to zero when the disorder strength increases. We show numerically that although the value of $γ$ strongly influences the statistical properties of transport parameters $Δ$ and of the energy level statistics, the form of their distributions always depends on the symmetry parameter $β$ even in the limit of strong disorder. In particular, the probability distribution is $p(Δ)\sim Δ^β$ when $Δ\to 0$ and $p(Δ) \sim \exp (-cΔ^2)$ in the limit $Δ\to\infty$.