The phase-dependent linear conductance of a superconducting quantum point contact

The exact expression for the phase-dependent linear conductance of a weakly damped superconducting quantum point contact is obtained. The calculation is performed by summing the complete perturbative series in the coupling between the electrodes, thus taking into account all possible multiple Andreev reflections inside the gap. The failure of any finite-order perturbative expansion in the limit of small voltage and small quasiparticle damping is analysed in detail. In the low-transmission regime this nonperturbative calculation yields a result which is at variance with standard tunnel theory. Our result exhibits an unusual phase dependence at low temperatures in qualitative agreement with the available experimental data.