Fermi gas

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 metals and semiconductors and neutrons in a neutron star can be approximated by treating them as Fermi gases. The energy distribution of the fermions in a Fermi gas in thermal equilibrium is determined by their density, temperature, and the set of available energy states, via Fermi-Dirac statistics.

By the Pauli principle, no quantum state can be occupied by more than one fermion (with identical properties); thus a Fermi gas, unlike a Bose gas, is prohibited from condensing into a Bose-Einstein condensate. Therefore the total energy of the Fermi gas at Absolute zero is larger than the sum of the single-particle ground states because the Pauli principle acts as an sort of interaction/pressure that keeps the fermions sepearated and moving. For this reason, the pressure of a Fermi gas is nonzero even at zero temperature, in contrast to that of a classical ideal gas. This so-called degeneracy pressure stabilizes a neutron star (a Fermi gas of neutrons) or a white dwarf star (a Fermi gas of electrons) against the inward pull of gravity, which would ostensibly collapse the star into a Black Hole. Only when a star is sufficiently massive to overcome the degeneracy pressure can it collapse into a singularity.

It is possible to define a Fermi temperature below which the gas can be considered degenerate (its pressure derives almost exclusively from the Pauli principle). This temperature depends on the mass of the fermions and the density of energy states. For metals, the electron gas's Fermi temperature is generally many thousands of kelvins, so in human applications they can be considered degenerate. The maximum energy of the fermions at zero temperature is called the Fermi energy. The Fermi energy surface in momentum space is known as the Fermi surface.

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 that deal with interaction (such as Fermi liquid theory or perturbation theory).

See also

• Bose gas
• Free electron model
• Gas in a box