QUANTUM NONLINEAR RESONANCE AND QUANTUM CHAOS IN AHARONOV-BOHM OSCILLATIONS IN MESOSCOPIC SEMICONDUCTOR RINGS

We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor r ing threaded by both a constant magnetic flux and a time-dependent, re sonant magnetic field with one or two frequencies. Working in the ball istic regime, we establish that the theory of ''quantum nonlinear reso nance'' applies, and thus that this system represents a possible solid -state realization of ''quantum nonlinear resonance'' and ''quantum ch aos.'' In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged ener gy exhibits sharp resonant behavior as a function of the applied const ant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequen cy. We compare and contrast the quantum chaos expected in these mesosc opic ''solid-state atoms'' with that observed in Rydberg atoms in micr owave fields, and discuss the prospects for experimental observation o f the effects we predict.