  We study a simplified Heisenberg spin model in order to clarify the idea of
decoherence in closed quantum systems. For this purpose, we define a new
concept: the decoherence function \Xi(t), which describes the dynamics of
decoherence in the whole system, and which is linked with the total (von
Neumann) entropy of all particles. As expected, decoherence is understood both
as a statistical process that is caused by the dynamics of the system, and also
as a matter of entropy. Moreover, the concept of decoherence time is applicable
in closed systems and we have solved its behaviour in the Heisenberg model with
respect to particle number N, density \rho and spatial dimension D in a 1/r
-type of potential. We have also studied the Poincare recurrences occurring in
these types of systems: in an N=1000 particle system the recurrence time is
close to the order of the age of the universe. This encourages us to conclude
that decoherence is the solution for quantum-classical problems not only in
practice, but also in principle.
