Trapping of an electron in the transmission through two quantum dots coupled by a wire

We consider single-channel transmission through a double quantum dot that consists of two identical single dots coupled by a wire. The numerical solution for the scattering wave function shows that the resonance width of a few of the states may vanish when the width (or length) of the wire and the energy of the incident particle take a certain value each. In such a case, a particle is trapped inside the wire as the numerical visualization of the scattering wave function shows. To understand these numerical results, we explore a simple model with a small number of states which allows to consider the problem analytically. If the eigenenergies of the closed system cross the energies of the transmission zeros, the wire effectively decouples from the rest of the system and traps the particle.