Quantum corrections to the conductance of a square quantum dot with soft confinement

We study the conductance of a square quantum dot, modeling the potential wi th a self-consistent Thomas-Fermi approximation. The resulting potential is characterized by level statistics indicative of mixed chaotic and regular electron dynamics within the dot in spite of the regular geometry of the ga tes defining the dot. We calculate numerically, for the case of a quantum d ot with soft confinement. the weak localization (WL) correction. We demonst rate tl-lat this confining potential may generate either Lorentzian or line ar lineshapes depending on the number of modes in the leads. Finally, we pr esent experimental WL data for a lithographically square dot and compare th e results with numerical calculations. We analyze the experimental results and numerical simulations in terms of semiclassical and random matrix theor y (RMT) predictions and discuss their limitations as far as real experiment al structures are concerned. Our results indicate that direct application o f the above predictions to distinguish between chaotic and regular dynamics in a particular cavity can not always lead to reliable conclusions as the shape and magnitude of the WL correction carl be strongly sensitive to the geometry-specific: non-universal features of the system.