# Resonance effects in quantum ballistic transport

## Abstract

The theory of coherent transmission resonances in multimode nanostructures is developed by considering a quasi-level, a decaying electron state localized within the structure, as primary, and deriving steady-state transmission and reflection probabilities versus energy as consequences. General (though not completely general) formulae are obtained for these as Lorentzian peaks and inverted peaks, in terms of the quasi-level decay lifetime and the mode fractions of the decay current. Both positive peaks and inverted peaks of the transmission probabilities equally are shown to be consequences of a decaying quasi-level. The dwell times, which determine the localized space charge for given occupations of the itinerant steady states, are obtained in terms of the same parameters, and it is shown that when all these states are filled through a resonance range of energy then the total localized space charge is equal to an electron charge times two (the spin degeneracy). A 'sum rule' is derived, giving the dwell time of each mode in terms of the phase-delay propagation times.