Unusual Bound States in Quantum Chains

The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges support bound solutions, in two or more dimensions. Here we find that the role of topology can be even more important than space availability, by showing the existence of bound solutions in one-dimensional systems such as quantum cross-chains and, in general, chains tied in geometries without loops. It is shown that these examples of unusual binding can be solved analitically for energies and eigenvectors. An experimental proposal is given in the form of tight-binding arrays of electromagnetic resonators, as the effects in question are of a wave-like nature.