  It is shown how classical states, meant as states representing a classical
object, can be produced in the thermodynamic limit, retaining the unitary
evolution of quantum mechanics. Besides, using a simple model of a single spin
interacting with a spin-bath, it is seen how decoherence, with the off-diagonal
terms in the density matrix going to zero, can be obtained when the number of
the spins in the bath is taken to go formally to infinity. In this case,
indeed, the system appears to flop at a frequency being formally infinity that,
from a physical standpoint, can be proved equivalent to a time average.
