Transport in the random Kronig-Penney model

TL;DR

This paper investigates the transport properties of the random Kronig-Penney model, revealing non-trivial quantum diffusion at critical energies despite a pure-point spectrum, due to vanishing Lyapunov exponents and density of states singularities.

Contribution

It provides new insights into quantum transport phenomena in disordered systems with critical energies where Lyapunov exponents vanish.

Findings

Quantum diffusion occurs at critical energies.

Lyapunov exponent vanishes at certain energies.

Density of states exhibits van Hove singularities.

Abstract

The Kronig-Penney model with random Dirac potentials on the lattice $\ZM$ has critical energies at which the Lyapunov exponent vanishes and the density of states has a van Hove singularity. This leads to a non-trivial quantum diffusion even though the spectrum is known to be pure-point.