  A method to determine the density and temperature of a system is proposed
based on quantum fluctuations typical of Bosons in the limit where the reached
temperature T is close to the critical temperature $T_c$ for a Bose condensate
at a given density $\rho$. Quadrupole and particle multiplicity fluctuations
relations are derived in terms of $\frac{T}{T_c}$. This method is valid for
weakly interacting infinite and finite Boson systems.
  As an example, we apply it to heavy ion collisions using the Constrained
Molecular Dynamics (CoMD) approach which includes the Fermi statistics. The
model shows some clusterization into deuteron and ${\alpha}$ clusters which
could suggest a Bose condensate. However, our approach demonstrates that in the
model there is no Bose condensate but it gives useful informations to be tested
experimentally. We stress the differences with methods based on classical
approximations. The derived 'quantum' temperatures are systematically higher
than the corresponding 'classical' ones. The role of the Coulomb charge of
fragments is discussed.
