Classical solutions of an electron in magnetized wedge billiards.

We have studied the classical solutions of a free electron constrained to move inside a circular wedge of angle theta(w), in the presence of a homogeneous constant magnetic field B. These billiards have broken rotational symmetry. As B and theta(w) are varied, the apex of the billiards affects the classical dynamics in an important way. We find that for billiards with angles (sqrt[5]-1)/2< or =theta(w)< or =pi/2, the dynamics exhibits a reentrant transition as the field increases. The transition is from regular-to-mixed-to-chaotic-to-mixed-to-chaotic regimes. The reentrance is connected to the appearance and disappearance of periodic orbits nucleated at the boundaries of these billiards as the field increases. There is no reentrance when theta(w)>pi/2. In the latter case as B increases the dynamics goes from quasiintegrable, to intermediate and then to chaotic whispering gallery Larmor modes.

Pauli principle and chaos in a magnetized disk.

We present results of a detailed quantum-mechanical study of a gas of N noninteracting electrons confined to a circular boundary and subject to homogeneous dc plus ac magnetic fields [B=B(dc)+B(ac)f(t), with f(t+2pi/omega(0))=f(t)]. We earlier found a one-particle classical phase diagram of the (scaled) Larmor frequency omega;(c)=omega(c)/omega(0) vs epsilon=B(ac)/B(dc) that separates regular from chaotic regimes. We also showed that the quantum spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in the transition from classically integrable to chaotic dynamics. Here we find that, as a function of N and (epsilon,omega(c)), there are clear quantum signatures in the magnetic response, when going from the single-particle classically regular to chaotic regimes. In the quasi-integrable regime the magnetization nonmonotonically oscillates between diamagnetic and paramagnetic as a function of N. We quantitatively understand this behavior from a perturbation theory analysis. In the chaotic regime, however, we find that the magnetization oscillates as a function of N but it is always diamagnetic. Equivalent results are also presented for the orbital currents. We also find that the time-averaged energy grows as N2 in the quasi-integrable regime but changes to a linear N dependence in the chaotic regime. In contrast, the results with Bose statistics are akin to the single-particle case and thus different from the fermionic case. We also give an estimate of possible experimental parameters where our results may be seen in semiconductor quantum dot billiards.

Holographic sundial.

We discuss a method of constructing white light holograms that can serve as sundials and in other applications. Arrangements with both digital and analog readouts are examined.