Fermi Gas - Ideal Fermi Gas

Ideal Fermi Gas

An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions. It is the quantum mechanical version of an ideal gas, for the case of fermionic particles. The behavior of electrons in a white dwarf or neutrons in a neutron star can be approximated by treating them as an ideal Fermi gas. Something similar can be done for periodic systems, such as electrons moving in the crystal lattice of metals and semiconductors, using the so called quasi-momentum or crystal momentum (Bloch wave). Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamics of an ideal Fermi gas reduces to the study of the behavior of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories that deal with interactions, e.g., using the perturbation theory.

The chemical potential of the (three dimensional) ideal Fermi gas is given by the following expansion (assuming ):

where E_F is the Fermi energy, k is the Boltzmann constant and T is temperature. Hence, the chemical potential is approximately equal to the Fermi energy at temperatures that are much lower than the characteristic Fermi temperature E_F/k. The characteristic temperature is on the order of 105 K for a metal, hence at room temperature (300 K), the Fermi energy and chemical potential are essentially equivalent. This is significant since it is the chemical potential, not the Fermi energy, which appears in the Fermi-Dirac statistics.