Real-Time Quantum Dynamics of a Single Spin 1/2 Coupled to a Spin Bath

We performed real-time dynamics of a spin 12 quantum system that is coupled to a bath of N quantum spin 12 particles. The quantities we study are the time dependence of the magnetization and of the quantum purity, P(t). If the spins that constitute the bath have no interactions with each other, the result is compared to a recent theoretical result. We also present simulations to study the effect of interactions between the bath spins. In particular, we analyze how P(t) approaches its asymptotic value for large t and N.