Supercurrent states in one-dimensional finite-size rings

We consider topological supercurrent excitations (SC's) in one-dimensional (1D) mesoscopic rings. In the superfluid phase such excitations are well defined except for (i) a tunneling between resonating states with clockwise and counterclockwise 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. Our approach, being based on the hydrodynamical action for the phase field and its generalization to the effective Hamiltonian, explicitly takes into account transitions between the states with different topological numbers and turns out to be very effective for the calculation of Delta and estimation of the decay width of SC, as well as for the unified description of all known 1D superfluid-insulator transitions. 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 fractional quantum Hall effect state and quasi-ID superconducting rings; We suggest some experimental setups for studying SC, e.g., via persistent current measurements, resonant electromagnetic absorption or echo signals, and relaxation of the metastable current states.