Shape-averaged weak localization in chaotic and integrable ballistic cavities

We perform magnetotransport measurements in ballistic cavities and obtained the average by small modulations on the shapes and/or on the Fermi level. We work with cavities whose underlying classical dynamics is chaotic (stadia and stomachs) and integrable (circles and rectangles). The former show a Lorentzian weak-localization peak, in agreement with semiclassical predictions and other averaging methods that have been used in recent measurements. For integrable cavities our measurements are in disagreement with the existing experimental results. These discrepancies illustrate the non-generic behaviour of scattering through integrable geometries that we analyse taking into account the interplay of integrability with smooth disorder and geometrical effects. The power spectra of the conductance fluctuations are also analysed, the deduced typical areas are in good agreement with those obtained from the weak localisation. The presence of periodic orbits in non-averaged Fourier transforms of the magnetoconductance for regular cavities indicates the good quality of our samples.