Quantum transport in chaotic and integrable ballistic cavities with tunable shape

We have performed 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 Sinaï billiards) 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 show that the shape of the weak localization is very sensitive to the exact geometry of the sample: a linear magnetoconductance has been observed for rectangles as expected by the theory for integrable cavities, whereas for circles the shape is always Lorentzian. These discrepancies illustrate the nongeneric behavior of scattering through integrable geometries, that we analyze taking into account the interplay of integrability with smooth disorder and geometrical effects. The power spectra of the conductance fluctuations are also analyzed, the deduced typical areas are in good agreement with those obtained from the weak localization. Periodic orbits in nonaveraged Fourier transforms of the magnetoconductance for regular cavities are clearly identified indicating the good quality of our samples.