  We study the behavior of a quantum gyroscope, that is, a quantum system which
singles out a direction in space in order to measure certain properties of
incoming particles such as the orientation of their spins. We show that
repeated Heisenberg interactions of the gyroscope with several incoming
spin-1/2 particles provides a simple model of decoherence which exhibits both
relaxation and dephasing. Focusing on the semiclassical limit, we derive
equations of motion for the evolution of a coherent state and investigate the
evolution of a superposition of such states. While a coherent state evolves on
a timescale given by the classical ratio of the angular momentum of the
gyroscope to that of the incoming particles, dephasing acts on a much shorter
timescale that depends only on the angular difference of the states in the
superposition.
