On the theory of systems with substitutional non-Hermitian disorder

Abstract

A novel family of disordered systems is proposed. This family belongs to the class of systems containing random substitutional non-Hermitian impurities. We limit our consideration to a rather simple case when the presence of substitutional point defects results in the model Hamiltonian featuring a diagonal disorder. In contrast to known models of non-Hermitian impurities, the nonzero density of states for each isolated from the host impurity is restricted to a continuous band of finite width. A method to construct corresponding impurity Hamiltonians is provided.