Avron J.E., Nemorovsky J
Quasienergies, Stark Hamiltonians and Growth of Energy
for Driven Quantum Rings
(20K, TeX)
ABSTRACT. We study time-dependent
Schroedinger operators in Aharonov-Bohm geometries
where the flux threading the hole increases linearly with time.
We show
that the 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.