Electron transport through a quantum cavity

Electron transport through a quantum cavity coupled with two one-dimensional waveguides is studied using a generalized scattering matrix method. In a symmetric N-channel cavity model, we are able to obtain an exact solution that predicts the electron energies at which the transmission of electron waves become zero. We found that the zero of transmission is closely related to the longitudinal resonance through inter-channel scattering, in particular, to the resonance of the highest propagating mode inside the cavity. This model provides a simple way to calculate the electron transmission through a cavity which could be useful in quantum waveguide engineering.