QUASI-ENERGIES, STARK-HAMILTONIANS, AND GROWTH OF ENERGY FOR DRIVEN QUANTUM RINGS

We study time-dependent Schrodinger operators in Aharonov-Bohm geometries where the flux threading the hole increases linearly with time. We show that the quasienergy operator has, in these cases, the same spectrum as the time-independent Stark Hamiltonian on the universal covering space. Combining known results on Stark Hamiltonians with a theorem of Bellissard, we prove that the energy of a particle on a finite ring, with smooth background potential, increases without bound as t --> infinity.