Density and temperature of fermions and bosons from quantum fluctuations

novel method to determine the density and temperature of a system constituted by fermions and/or bosons is proposed based on quantum fluctuations. For fermions system, the results in the limit where the reached temperature T is small and where there is no constraint for the reached temperature T compared to the Fermi energy εf at a given density ρ are given, respectively. Quadrupole and multiplicity fluctuation relations are derived in terms of T/εf. We compared the two set results in the limit when T is much smaller compared to Fermi energy εf and they are consistent, as expected. The classical limit is also obtained for high temperatures and low densities. For bosons system, quadrupole and multiplicity fluctuations using Landau's theory of fluctuations near the critical point for a Bose-Einstein condensate (BEC) at a given density ρ are derived. As an example, we apply our approach to heavy ion collisions using the Constrained Molecular Dynamics model (CoMD) which includes the fermionic statistics. The multiplicity fluctuation quenching for fermions is found in the model and confirmed by experimental data. To reproduce the available experimental data better, we propose a modification of the collision term in the approach to include the possibility of α−αcollisions. The relevant Bose-Einstein factor in the collision term is properly taken into account. This approach increases the yields of bosons relative to fermions closer to data. Boson fluctuations become larger than one as expected.