# Fermi gas

A

**Fermi gas** is a collection of non-interacting

fermions. It is therefore the quantum mechanical version of the concept of a classical

ideal gas, for the case of fermionic particles. Examples include electrons in metals and semiconductors (when the Coulomb interaction between them is neglected), as well as

neutrons in a neutron star (again when neglecting the interaction). The energy-distribution of the fermions in a Fermi gas in thermal equilibrium is determined by their number (or density), the temperature and the set of available energy states, via

Fermi-Dirac statistics. As no energy state can be occupied by more than one fermion (

Pauli principle), the total energy of the Fermi gas at zero temperature is larger than the product of the number of particles and the single-particle ground state energy. For the same reason, the pressure of a Fermi gas is nonzero even at zero temperature, in contrast to that of a classical

ideal gas (which would be zero). This so-called

degeneracy pressure stabilizes a

neutron star (Fermi gas of neutrons) or a

White Dwarf star (Fermi gas of electrons) against the inward pull of gravity.

Since interactions are neglected by definition, the problem of treating the equilibrium properties and dynamical behaviour of a Fermi gas reduces to the study of the behaviour of single independent particles. As such, it is still relatively tractable and forms the starting point for more advanced theories (such as Fermi liquid theory or perturbation theory in the interaction) which take into account interactions to some degree of accuracy.