10 research outputs found
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
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]