  Motivated by fundamental questions about the loss of phase coherence at low
temperature we consider relaxation, dephasing and renormalization effects in
quantum two-level systems which are coupled to a dissipative environment. We
observe that experimental conditions, e.g., details of the initial state
preparation, determine to which extent the environment leads to dephasing or to
renormalization effects. We analyze an exactly solvable limit where the
relation between both can be demonstrated explicitly. We also study the effects
of dephasing and renormalization on response functions.
