  We consider topological supercurrent excitations (SC) in 1D mesoscopic rings.
Under certain conditions such excitations are well-defined except for (i) a
tunneling between resonating states with clockwise and anti-clockwise currents,
which may be characterized by the amplitude $\Delta$, and (ii) a decay of SC
assisted by phonons of the substrate, both effects being macroscopically small.
Most attention is paid to the calculation of the macroscopic scaling of
$\Delta$ (the main superfluid characteristic of a mesoscopic system) under
different conditions: a commensurate system, a system with single impurity, and
a disordered system. The results are in a very good agreement with the
exact-diagonalization spectra of the boson Hubbard models.
  Apart from really 1D electron wires we discuss two other important
experimental systems: the 2D electron gas in the FQHE state and quasi-1D
superconducting rings. We suggest some experimental setups for studying SC,
e.g., via persistent current measurements, resonant electro-magnetic absorption
or echo signals, and relaxation of the metastable current states.
