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The Effect of Quantum Phase Slip Interactions on the Transport of Thin Superconducting Wires

We study theoretically the effect of interactions between quantum phase slips in a short superconducting wire beyond the dilute phase slip approximation. In contrast to the smooth transition in dissipative Josephson junctions, our analysis shows that treating these interactions in a self consistent manner leads to a very sharp transition with a critical resistance of $R_Q= h/(4e^2)$. The addition of the quasi-particles resistance at finite temperature leads to a quantitative agreement with recent experiments on short MoGe nanowires. Our treatment is complementary to the theory of the thermal activation of phase slips, which is only valid for temperature at the vicinity of the mean field metal to superconductor transition. This self consistent treatment should also be applicable to other physical systems that can be mapped onto similar sine-Gordon models, in the intermediate-coupling regime.