  The stable and metastable states of different configurations of a loop in the
form of an eight is studied in the presence of a magnetic field. We find that
for certain configurations the current is equal to zero for any value of the
magnetic field leading to a magnetic field independent superconducting state.
The state with fixed phase circulation becomes unstable when the momentum of
the superconducting electrons reaches a critical value. At this moment the
kinetic energy of the superconducting condensate becomes of the same order as
the potential energy of the Cooper pairs and it leads to an instability.
Numerical analysis of the time-dependent Ginzburg-Landau equations shows that
the absolute value of the order parameter changes gradually at the transition
from a state with one phase circulation to another although the vorticity
change occurs abruptly.

Superconductivity