Resonant multiple Andreev reflections in mesoscopic superconducting junctions

We investigate the properties of subharmonic gap structure (SGS) in superconducting quantum contacts with normal-electron resonances. We find two distinct features of the SGS in resonant junctions which distinguish them from nonresonant point contacts: (i) The odd-order structures on the current-voltage characteristics of resonant junctions are strongly enhanced and have pronounced peaks, while the even-order structures are suppressed, in the case of a normal electron resonance being close to the Fermi level. (ii) Huge current peaks develop at $eV=\pm {2E}_0$ where $E_0$ indicates the distance of the resonance to the Fermi level. These properties are determined by the effect of narrowing of the resonance during multiple Andreev reflections and by overlap of electron and hole resonances.