  We investigate the resistively shunted Josephson junction (RSJ), using the
stochastic Liouville equation method in imaginary time - an exact scheme based
on the Feynman-Vernon influence functional. The formulation we use makes it
clear that Schmid's superconducting - insulating quantum phase transition long
believed to occur in the RSJ is forbidden already at the qualitative level.
This confirms theoretically a similar conclusion based on experimental
observations drawn in 2020 by Murani et al. For all parameters investigated, we
find that shunting a junction makes it more superconducting. We reveal that the
UV cutoff of the resistor plays an unforeseen key role in these systems, and
show that the erroneous prediction of an insulating state resulted from
ill-assuming it would not.
