  We introduce phase disorder in a 1D quantum resistor through the formal
device of `fake channels' distributed uniformly over its length such that the
out-coupled wave amplitude is re-injected back into the system, but with a
phase which is random. The associated scattering problem is treated via
invariant imbedding in the continuum limit, and the resulting transport
equation is found to correspond exactly to the Lloyd model. The latter has been
a subject of much interest in recent years. This conversion of the random phase
into the random Cauchy potential is a notable feature of our work. It is
further argued that our phase-randomizing reservoir, as distinct from the well
known phase-breaking reservoirs, induces no decoherence, but essentially
destroys all interference effects other than the coherent back scattering.
