  Superconducting properties of metallic nano-wires may strongly depend on
specific experimental conditions. Here we consider a setup where
superconducting phase fluctuations are restricted at one point inside the wire
and equilibrium supercurrent flows along the wire segment of an arbitrary
length $L$. Low temperature physics of this structure is essentially
determined, on one hand, by smooth phase fluctuations and, on the other hand,
by quantum phase slips. The zero temperature phase diagram is controlled by the
wire cross section and consists of a truly superconducting phase and two
different phases where superconductivity can be observed only at shorter length
scales. One of the latter phases exhibits more robust short-scale
superconductivity whereas another one demonstrates a power-law decay of the
supercurrent with increasing $L$ already at relatively short scales.
