TRANSITION BETWEEN DIFFERENT QUANTUM STATES IN A MESOSCOPIC SYSTEM - THE SUPERCONDUCTING RING

We investigate the thermodynamic properties of a superconducting ring, both analytically and numerically relying upon the Ginzburg-Landau th eory. We find that modulated solutions for the order parameter play a role in describing the thermodynamic transitions between consecutive m odes of uniform order parameter, associated with different quantum num bers. Exact expressions for these solutions are given in terms of elli ptic functions. We identify the family of energy extrema which, being saddle points of the energy in the functional space of the distributio ns of the order parameter, represent the energy barrier to be overcome for transitions between different solutions.