Diffraction and quasiclassical limit of the Aharonov--Bohm effect

Since the Aharonov-Bohm effect is the purely quantum effect that has no analogues in classical physics, its persistence in the quasiclassical limit seems to be hardly possible. Nevertheless, we show that the scattering Aharonov-Bohm effect does persist in the quasiclassical limit owing to the diffraction, i.e. the Fraunhofer diffraction in the case when space outside the enclosed magnetic flux is Euclidean, and the Fresnel diffraction in the case when the outer space is conical. Hence, the enclosed magnetic flux can serve as a gate for the propagation of short-wavelength, almost classical, particles. In the case of conical space, this quasiclassical effect which is in principle detectable depends on the particle spin.Comment: 12 pages, minor changes, references update

Quantum chaos in a deformable billiard: Applications to quantum dots

We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple conformal maps of the unit disk; the shape of this family of billiards may be varied continuously at fixed area by tuning the parameters of the map. The classical dynamics of these billiards is well-understood and this allows us to study the quantum properties of subfamilies which span the transition from integrability to chaos as well as families at approximately constant degree of chaoticity (Kolmogorov entropy). In the regime of hard chaos we find that the statistical properties of interest are well-described by random-matrix theory and completely insensitive to the particular shape of the dot. However in the nearly-integrable regime non-universal behavior is found. Specifically, the level-width distribution is well-described by the predicted $\chi^2$ distribution both in the presence and absence of magnetic flux when the system is fully chaotic; however it departs substantially from this behavior in the mixed regime. The chaotic behavior corroborates the previously predicted behavior of the peak-height distribution for deformed quantum dots. We also investigate the energy-level correlation functions which are found to agree well with the behavior calculated for quasi-zero-dimensional disordered systems.Comment: 25 pages (revtex 3.0). 16 figures are available by mail or fax upon request at [email protected]