In this paper, we investigate a mesoscopic ring by making use of the imaginary-time path-integral method. With the help of the invariant theory, an expression for the Aharonov-Anadan phase is found and the condition for the validity of the adiabatic approximation is then discussed. Finally, we study the special case of cylindrically symmetrical magnetic field.

• Received 5 April 1993

DOI:https://doi.org/10.1103/PhysRevB.48.11401