Absence of a dissipative quantum phase transition in Josephson junctions: Theory

We obtain the reduced density matrix of a resistively shunted Josephson junction (RSJ), using the stochastic Liouville equation method in imaginary time - an exact numerical scheme based on the Feynman-Vernon influence functional. For all parameters investigated, we find that shunting a junction makes it more superconducting. We find no trace of the Schmid superconducting-insulating quantum phase transition long believed to occur in the RSJ. This work confirms theoretically a similar conclusion drawn in 2020 by Murani et al., based on experimental observations. We reveal that resistors with no UV cutoff always yield a fully localized phase and we explain how previous works predicting an insulating state came to obtain a contrary result.