Ordered (extreme value) statistics of energy levels for 1D disordered quantum mechanics
- Christophe Texier,
Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder
J. Phys. A: Math. Gen. 33, 6095-6128 (2000).
Dirac equation with a random mass is known to support a critical extended state at zero energy (note that Dirac operator is directly related to the supersymmetric Schrödinger Hamiltonian). We analyse the average density of states for 1D Dirac operator in a bounded domain. Due to delocalisation, the DoS is sensitive to the boundaries for E → 0. This provides a possible definition of the localisation length, much larger than the inverse localisation length, that usually provides a definition of localisation in 1D problems. We argue that Lyapunov exponent is not able to capture the essential physics of low energy localisation near the delocalisation point (E=0).