Complex energies of open one-dimensional disordered wires

Abstract

We study statistical properties of complex eigenvalues of a non-Hermitian Hamiltonian describing open one-dimensional (1D) models with various types of diagonal disorder. We consider the case of 1D tight-binding wires, with both on-site uncorrelated and correlated disorder, coupled to the continuum through leads attached to the wire edges. In particular, we focus on the location of the eigenvalues in the complex plane as a function of the coupling strength and the disorder strength. Specific interest is paid to the super-radiance transition emerging at the perfect coupling between wire and leads.