Density of states in the non-Hermitian Lloyd model

We reconsider the recently proposed connection between density of states in the so-called “non-Hermitian quantum mechanics” and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-Hermitian random “Hamiltonian.” However, finding the density of states of a non-Hermitian random Hamiltonian remains an open problem, contrary to previous findings in the literature.