  The molecular states of conduction electrons in laterally coupled quantum
rings are investigated theoretically. The states are shown to have a distinct
magnetic field dependence, which gives rise to periodic fluctuations of the
tunnel splitting and ring angular momentum in the vicinity of the ground state
crossings. The origin of these effects can be traced back to the Aharonov-Bohm
oscillations of the energy levels, along with the quantum mechanical tunneling
between the rings. We propose a setup using double quantum rings which shows
that Aharonov-Bohm effects can be observed even if the net magnetic flux
trapped by the carriers is zero.
