The Landau-Zener Model with Decoherence: The case S=1/2

We study the dynamics of a spin coupled to an oscillating magnetic field, in the presence of decoherence and dissipation. In this context we solve the master equation for the Landau-Zener problem, both in the unitary and in the irreversible case. We show that a single spin can be "magnetized" in the direction parallel to the oscillating bias. When decay from upper to lower level is taken into account, hysteretic behavior is obtained.