  We study the magneto-transport in Aharonov-Bohm (AB) billiards forming doubly
connected structures. In these systems, non-averaged conductance oscillates as
a function of magnetic flux with period h/e. We derive formulas of the
correlation function C of the magneto-conductance for chaotic and regular AB
billiards by use of the semiclassical theory. The different higher harmonics
behaviors for C are related to the differing distribution of classical dwelling
times. The AB oscillation in ballistic regimes provides an experimental probe
of quantum signatures of classical chaotic and regular dynamics.
