A Fermi gas is an idealized model, an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin.

The Sommerfeld expansion provides a systematic way of expanding these expressions in powers of \(T\) and is an important analytical tool in analyzing the low temperature properties of the ideal Fermi gas (IFG).

Ideal Fermi gas The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: kBT µ, βµ 1 , which defines the degenerate Fermi gas. In this limit, the quantum mechanical nature of the system becomes especially important, and the system has little to do with the classical ideal gas.

We say that the particles have condensed into the state with energy ε ∗ 0. The quantity n ∗ 0 is the condensate density. The remaining particles, with density n ′, are said to comprise the overcondensate. With the total density n fixed, we have n = n ∗ 0 + n ′.

We discuss basic properties of a gas of fermions at low temperature. We shall get some intuition about what the particles are doing by examining the Fermi-Dirac distribution function. We shall find the energy of the gas, and the pressure at zero temperature, finding that it is surprisingly high (not zero as one might guess).

This is called degeneracy pressure, and it is the characteristic feature of a Fermi gas. All three of these gases--the classical ideal gas, the Bose gas, and the Fermi gas--are composed of particles that move around as you'd expect.

Some terminology: “Fermi gas” refers to a noninteracting or weakly-interacting gas of Fermions, which at low temperatures will exhibit a Fermi surface due to Pauli exclusion.

Explains free fermions, properties, specific heat, white dwarf and neutron star, bond theory, diodes, non-viscous hydrodynamics, diffusion, continuity equation with diffusion, heat conduction, transport in a metal, hall effect, Boltzmann equation, Einstein relations, noise and noise spectrum.

May 27, 2024 · A Fermi gas is an ensemble of a large number of fermions, particles that are subject to the Pauli Exclusion Principle. This principle states that no two fermions can occupy the same quantum state simultaneously.

Why is it that particles with half-integer spin are Fermi particles whereas particles with integer spin are Bose particles? An explanation has been worked out by Pauli from complicated arguments from quantum field theory and relativity.