The effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian

Abstract

The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0, L] is derived. Our method relies on the eigenvalue distributions (extreme value statistics problem) which are obtained explicitly. The well-known Dyson singularity is recovered above the crossover energy . Below ϵc we find a log-normal suppression of the average DoS .