Bose–Einstein vs Fermi–Dirac
Bose–Einstein statistics describes indistinguishable particles of integer spin (bosons): photons, gluons, gravitons, helium-4 atoms. Mean occupation ni = 1/(e(εi−μ)/kBT − 1). Bosons can occupy the same quantum state, giving Bose–Einstein condensates below the critical temperature.
Fermi–Dirac statistics describes indistinguishable half-integer-spin particles (fermions): electrons, protons, neutrons, quarks, helium-3 atoms. Mean occupation ni = 1/(e(εi−μ)/kBT + 1). Pauli exclusion forbids any two fermions sharing a quantum state, which underlies atomic structure, white-dwarf and neutron-star degeneracy pressure, and the periodic table.
Both reduce to the classical Maxwell–Boltzmann distribution at high temperature/low density. The sign in the denominator is the only formal difference.
Recent research on this topic from arXiv
Preprints and papers indexed on arXiv.org. Links open the public abstract pages.
- Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics
Robert K. Niven · 2004 ·arXiv:0412460v2
The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explici... - Multi-parameter Fermi-Dirac and Bose-Einstein Stochastic Distributions
Fridolin Melong, Mahouton Norbert Hounkonnou · 2023 ·arXiv:2305.18194v1
In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties, namel... - Bose-Einstein and Fermi-Dirac Interferometry in Particle Physics
Gideon Alexander · 2003 ·arXiv:0302130v1
The application of the Bose-Einstein and Fermi-Dirac interferometry to multi-hadron final states of particle reactions is reviewed. The underlying theoretical concepts of particle interferometry is presented where a special emphasis is give... - What is between Fermi-Dirac and Bose-Einstein Statistics?
Krzysztof Byczuk, Jozef Spalek, Geoffrey Joyce et al. · 2004 ·arXiv:0403735v1
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution...
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