Density and Temperature of Fermions
from Quantum
Fluctuations, H. Zheng,
Cyclotron Institute, Texas
A&M
University, College Station, Texas USA − A novel method to
determine the
density and temperature of a system based on quantum fluctuations
typical of
Fermions is generalized to the limit where the reached temperature
T is large
compared to the Fermi energy ϵ_{f} at a given
density ρ. Quadrupole
and particle
multiplicity fluctuations relations are derived in terms of T/ϵ_{f}. The relevant
Fermi integrals
are numerically solved for any values of T/ϵ_{f} and
compared to the
analytical approximations. The
classical
limit is obtained, as expected, in the limit of large temperatures
and small densities.
We propose simple
analytical formulas
which reproduce the numerical results, valid for all values of T/ϵ_{f}.