FermiDiracjakauman

Fermi-Dirac distribution is a statistical distribution used in quantum statistics to describe the distribution of particles over energy states in systems composed of many indistinguishable particles that obey the Pauli exclusion principle. This principle states that no two fermions can occupy the same quantum state simultaneously. The Fermi-Dirac distribution is named after the physicists Enrico Fermi and Paul Dirac, who independently developed it in the 1920s.

The distribution is given by the formula:

f(E) = 1 / (exp((E - μ) / kT) + 1)

where:

- f(E) is the probability that a state at energy E is occupied,

- E is the energy of the state,

- μ is the chemical potential, which is a measure of the available energy per particle,

- k is the Boltzmann constant,

- T is the temperature.

At absolute zero temperature (T = 0 K), the Fermi-Dirac distribution simplifies to a step function, where all states with energy less than the chemical potential are occupied, and all states with energy greater than the chemical potential are empty. This is known as the Fermi sea. As the temperature increases, the distribution becomes more spread out, and the occupation of states above the chemical potential becomes more probable.

The Fermi-Dirac distribution is fundamental in understanding the behavior of electrons in metals and semiconductors, as well as in the study of neutron stars and other systems of fermions. It is also used in the context of Bose-Einstein statistics for bosons, which do not obey the Pauli exclusion principle.