The effect of boundaries on the spectrum of a one-dimensional random mass Dirac Hamiltonian
Résumé
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 explicitly obtained. The well-known Dyson singularity \sim-L/|epsilon|ln^3|\epsilon| is recovered above the crossover energy epsilon_c\sim exp-sqrt{L}. Below epsilon_c we find a log-normal suppression of the average DoS \sim 1/(|epsilon|sqrt(L))exp(-(ln^2|epsilon|)/L).