Classical states and decoherence produced by unitary evolution in the thermodynamic limit

It is shown how classical states, meaning states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Also, 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 that is formally infinity that, from a physical standpoint, can be proved equivalent to a time average.