  Superconducting nanowires are the dual elements to Josephson junctions, with
quantum phase-slip processes replacing the tunneling of Cooper pairs. When the
quantum phase-slip amplitude ES is much smaller than the inductive energy EL,
the nanowire responds as a superconducting inductor. When the inductive energy
is small, the response is capacitive. The crossover at low temperatures as a
function of ES/EL is discussed and compared with earlier experimental results.
For one-dimensional and two-dimensional arrays of nanowires quantum phase
transitions are expected as a function of ES/EL. They can be tuned by a
homogeneous magnetic frustration.
