Dissipative death of quantum coherences in a spin system

We investigate the influence of weak dissipation on the dynamics of a kicked spin system. Compared to its classical limit the quantum system is strongly affected by small dissipation. We present the attenuation of two different intrinsically quantum phenomena, recurrencies and tunneling. We find agreement of analytical perturbative estimates and numerical results. We further show that dissipation acts quite differently on the quantum evolution depending on whether we are in a classically chaotic or regular domain.