  We discuss some aspects related to the so-called Hilbert space Average
Method, as an alternative to describe the dynamics of open quantum systems.
First we present a derivation of the method which does not make use of the
algebra satisfied by the operators involved in the dynamics, and extend the
method to systems subject to a Hamiltonian that changes with time. Next we
examine the performance of the adiabatic quantum search algorithm with a
particular model for the environment. We relate our results to the criteria
discussed in the literature for the validity of the above-mentioned method for
similar environments.
