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 eigenvalues distributions (extreme value statistics problem) which are explicitly obtained. The well-known Dyson singularity <rho(epsilon;L)>\sim-L/|epsilon|ln^3|ε| 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 <rho(epsilon;L)> \sim 1/(|epsilon|sqrt(L))exp(-(ln^2|epsilon|)/L).

13 pages, 2 figures; v2 minor corrections

References in corpus (2)

• Sinai model in presence of dilute absorbers
• One-dimensional classical diffusion in a random force field with weakly concentrated absorbers

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