  We preset a variant of the Caldeira-Leggett (CL) model of a harmonic
oscillator coupled to an environment. The CL model is a standard tool for
studying the physics of decoherence. Our "adapted Caldeira-Leggett" (ACL) model
is built in a finite Hilbert space which makes it suitable for numerical
studies. Taking a numerical approach allows us to avoid the limitations of
standard approximation schemes used with the CL model. We are able to evolve
the ACL model in a fully reversible unitary manner, without the built-in time
asymmetry and other assumptions that come with the master equation methods
typically used. We have used the ACL model to study new topics in the field of
decoherence and einselection where the full unitary evolution is essential to
our work. Those results (reported in companion papers) include an examination
of the relationship between einselection and the arrow of time, and studies of
the very earliest stages of einselection. This paper provides details about the
ACL model and our numerical methods. Our numerical approach makes it
straightforward to explore and plot any property of the physical system. Thus
we believe the examples and illustrations we present here may provide a helpful
resource for those wishing to improve their familiarity with standard
decoherence results, as well as those looking to probe the underpinnings of our
companion papers. We expect the ACL model will be a useful tool for exploring
additional phenomena that cannot be studied using traditional approximation
schemes.
