Quantum fluctuations cause a decay of the supercurrent ill thin superconducting wires making them resistive even at very low temperatures. We derive a microscopic effective action formalism that goes beyond the usual TDGL approach and study quantum fluctuations of the superconducting order parameter at all temperatures below Tc. We calculate the quantum phase slip rate in thin superconducting wires, demonstrate the importance of dissipation in a quantum phase slip process, and evaluate the resistance R(T) of the wire. In very thin wires the effect is well observable, even at zero temperature.
Zaikin, A. D., Golubev, D. S., van Otterlo, A., & Zimanyi, G. T. (1996). Quantum decay of supercurrent in thin superconducting wires. Czechoslovak Journal of Physics, 46(SUPPL. 2), 571–572. https://doi.org/10.1007/BF02583593