We study quantum phase-slip (QPS) processes in a superconducting ring
containing N Josephson junctions and threaded by an external static magnetic
flux. In a such system, a QPS consists of a quantum tunneling event connecting
two distinct classical states of the phases with different persistent currents
[K. A. Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson
coupling energy EJ of the junctions is larger than the charging energy EC =
e2/2C where C is the junction capacitance, the quantum amplitude for the QPS
process is exponentially small in the ratio EJ/EC. At given magnetic flux each
QPS can be described as the tunneling of the phase difference of a single
junction of almost 2pi, accompanied by a small harmonic displacement of the
phase difference of the other N-1 junctions. As a consequence the total QPS
amplitude nu is a global property of the ring. Here we study the dependence of
nu on the ring size N taking into account the effect of a finite capacitance C0
to ground which leads to the appearance of low-frequency dispersive modes.
Josephson and charging effects compete and lead to a nonmonotonic dependence of
the ring critical current on N. For N=infty, the system converges either
towards a superconducting or an insulating state, depending on the ratio
between the charging energy E0 = e2/2C0 and the Josephson coupling energy EJ.Comment: (19 pages, 12 figures) The final version deviated from the original
version. One of the author was removed from the lis
