Transition between different quantum states in a mesoscopic system: The superconducting ring.

Abstract

We investigate the thermodynamic properties of a superconducting ring, both analytically and numerically, relying upon the Ginzburg-Landau theory. We find that modulated solutions for the order parameter play a role in describing the thermodynamic transitions between consecutive modes of uniform order parameter, associated with different quantum numbers. Exact expressions for these solutions are given in terms of elliptic functions. We identify the family of energy extrema which, being saddle points of the energy in the functional space of the distributions of the order parameter, represent the energy barrier to be overcome for transitions between different solutions. {copyright} {ital 1996 The American Physical Society.}