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For both Bose–Einstein and Maxwell–Boltzmann statistics, more than one particle can occupy the same state, unlike Fermi–Dirac statistics. Equilibrium thermal distributions for particles with integer spin (bosons, red), half integer spin (fermions, blue), and classical (spinless) particles (green).
Fermi–Dirac statistics applies to fermions (particles that obey the Pauli exclusion principle), and Bose–Einstein statistics applies to bosons. As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit, unless they also have a very high density, as for a white dwarf .
There are important differences between the statistical behavior of bosons and fermions, which are described by Bose–Einstein statistics and Fermi–Dirac statistics respectively. Roughly speaking, bosons have a tendency to clump into the same quantum state, which underlies phenomena such as the laser , Bose–Einstein condensation , and ...
This is the first quantization approach and historically Bose–Einstein and Fermi–Dirac correlations were derived through this wave function formalism. In high-energy physics , however, one is faced with processes where particles are produced and absorbed and this demands a more general field theoretical approach called second quantization .
All subatomic particles must be one or the other. A composite particle may fall into either class depending on its composition. In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-odd-integer spin (spin 1 / 2 , spin 3 / 2 , etc.) and obey the Pauli exclusion principle.
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics, and considering the limit of a very large box, the Thomas–Fermi approximation (named after Enrico Fermi and Llewellyn Thomas) is used to express the degeneracy of the energy states as a differential, and summations over states ...
All known particles obey either Fermi–Dirac statistics or Bose–Einstein statistics. A particle's intrinsic spin always predicts the statistics of a collection of such particles and conversely: [3] integral-spin particles are bosons with Bose–Einstein statistics, half-integral-spin particles are fermions with Fermi–Dirac statistics.
Fermionic condensate: Similar to the Bose-Einstein condensate but composed of fermions, also known as Fermi-Dirac condensate. The Pauli exclusion principle prevents fermions from entering the same quantum state, but a pair of fermions can be bound to each other and behave like a boson, and two or more such pairs can occupy quantum states of a ...