  We present a rigorous analysis of the phenomenon of decoherence for general
$N-$level systems coupled to reservoirs. The latter are described by free
massless bosonic fields. We apply our general results to the specific cases of
the qubit and the quantum register. We compare our results with the explicitly
solvable case of systems whose interaction with the environment does not allow
for energy exchange (non-demolition, or energy conserving interactions). We
suggest a new approach which applies to a wide variety of systems which are not
explicitly solvable.
