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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 .
To exhibit Bose–Einstein condensation, the fermions must "pair up" to form bosonic compound particles (e.g. molecules or Cooper pairs). The first molecular condensates were created in November 2003 by the groups of Rudolf Grimm at the University of Innsbruck, Deborah S. Jin at the University of Colorado at Boulder and Wolfgang Ketterle at MIT.
Similarly the Bose–Einstein correlations between two neutral pions are somewhat stronger than those between two identically charged ones: in other words two neutral pions are “more identical” than two negative (positive) pions. The surprising nature of these special Bose–Einstein correlations effects made headlines in the literature. [5]
The name boson was coined by Paul Dirac [3] [4] to commemorate the contribution of Satyendra Nath Bose, an Indian physicist. When Bose was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh), [5] [6] he and Albert Einstein developed the theory characterising such particles, now known as Bose–Einstein statistics and Bose–Einstein condensate.
Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in relativistic quantum field theory, particles with integer spin are bosons.
These statistical properties are described as Bose–Einstein statistics. Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. Systems of many identical fermions are described by Fermi–Dirac statistics.
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).
All elementary particles are either bosons or fermions. These classes are distinguished by their quantum statistics: fermions obey Fermi–Dirac statistics and bosons obey Bose–Einstein statistics. [1] Their spin is differentiated via the spin–statistics theorem: it is half-integer for fermions, and integer for bosons.