Christophe Texier 1, 2, Christian Hagendorf 3
Journal of Physics A General Physics 43 (2010) 025002
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).
- 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI – Paris Sud - 2. Laboratoire de Physique des Solides (LPS),
CNRS : UMR8502 – Université Paris XI – Paris Sud - 3. Laboratoire de Physique Théorique de l’ENS (LPTENS),
CNRS : UMR8549 – Université Paris VI – Pierre et Marie Curie – Ecole Normale Supérieure de Paris – ENS Paris