Quantum chaotic transport in ballistic Aharonov-Bohm billiards

We study the magneto-transport properties of single ballistic Aharonov-Bohm (AB) billiards. The wave-number averaged reflection probability is calculated by use of the semiclassical scattering theory within the diagonal approximation. The existence of oscillation of magneto-conductance, analogous to the Alʹtshuler-Aronov-Spivak effect in disordered metal rings, is theoretically predicted for experimentally-realizable ballistic AB billiards. Chaotic and integrable (and mixed) classical billiards have turned out to lead to qualitatively different semiclassical formulas for conductance with their behavior determined only by knowledge regarding the underlying classical scatterings.