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

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

2009-09-11

arxiv.org/abs/0909.2205v2

J. Phys. A: Math. Theor. 43 (2010) 025002

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages, 2 figures; v2 minor corrections

Scientific paper

10.1088/1751-8113/43/2/025002

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).

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