  Within the density matrix formalism, it is shown that a simple way to get
decoherence is through the introduction of a "quantum" of time (chronon): which
implies replacing the differential Liouville--von Neumann equation with a
finite-difference version of it. In this way, one is given the possibility of
using a rather simple quantum equation to describe the decoherence effects due
to dissipation. Namely, the mere introduction (not of a "time-lattice", but
simply) of a "chronon" allows us to go on from differential to
finite-difference equations; and in particular to write down the
quantum-theoretical equations (Schroedinger equation, Liouville--von Neumann
equation,...) in three different ways: "retarded", "symmetrical", and
"advanced". One of such three formulations --the retarded one-- describes in an
elementary way a system which is exchanging (and losing) energy with the
environment; and in its density-matrix version, indeed, it can be easily shown
that all non-diagonal terms go to zero very rapidly. [A much larger
presentation of the theoretical ground on which this paper is based appeared in
the e-print quant-ph/9706059, and in the preprint IC/98/74, ICTP; Trieste,
1998].
