Weak localization and integrability in ballistic cavities

We demonstrate the existence of an interference contribution to the average magnetoconductance, G{}(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G{}(B) is qualitatively different for chaotic and regular cavities (saturation versus linear increase) which is explained semiclassically by the differing classical distribution of areas. The magnitude of G{}(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor); interference between trajectories which are not exactly time reversed must be included.