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

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 eigenvalues distributions (extreme value statistics problem) which are obtained explicitly. The well-known Dyson singularity %( ;L) ∼ − L | | ln3 | | is recovered above the crossover energy c ∼ exp− √ L. Below c we find a log-normal suppression of the average DoS %( ;L) ∼ 1 | |L exp(− 1 L ln 2 | |).