Chiral and nonorthogonal eigenstate pairs in open quantum systems with weak backscattering between counterpropagating traveling waves

We study the properties of energy eigenstates in open quantum systems in which clockwise and counterclockwise traveling waves are weakly coupled. We show that under rather general conditions the energy eigenstates of such systems can appear in pairs of nonorthogonal, copropagating traveling-wave states. The relation to exceptional points of the effective non-Hermitian Hamiltonian is discussed.