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In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting indistinguishable particles may occupy a set of available discrete energy states, at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose. The Bose–Einstein statistics apply only to those particles not limited to single occupancy of the same state—that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of spin and are named bosons, after the statistics that correctly describe their behaviour. There must also be no significant interaction between the particles. ==Concept== At low temperatures, bosons behave differently from fermions (which obey the Fermi–Dirac statistics) in a way that an unlimited number of them can "condense" into the same energy state. This apparently unusual property also gives rise to the special state of matter – Bose Einstein Condensate. Fermi–Dirac and Bose–Einstein statistics apply when quantum effects are important and the particles are "indistinguishable". Quantum effects appear if the concentration of particles satisfies, : where ''N'' is the number of particles and ''V'' is the volume and ''n''''q'' is the quantum concentration, for which the interparticle distance is equal to the thermal de Broglie wavelength, so that the wavefunctions of the particles are barely overlapping. Fermi–Dirac statistics apply to fermions (particles that obey the Pauli exclusion principle), and Bose–Einstein statistics apply to bosons. As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit unless they have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration. B–E statistics was introduced for photons in 1924 by Bose and generalized to atoms by Einstein in 1924–25. The expected number of particles in an energy state ''i'' for B–E statistics is : with ''εi'' > ''μ'' and where ''ni'' is the number of particles in state ''i'', ''gi'' is the degeneracy of state ''i'', ''εi'' is the energy of the ''i''th state, ''μ'' is the chemical potential, ''k'' is the Boltzmann constant, and ''T'' is absolute temperature. For comparison, the average number of fermions with energy given by Fermi–Dirac particle-energy distribution has a similar form, : B–E statistics reduces to the Rayleigh–Jeans Law distribution for , namely . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bose–Einstein statistics」の詳細全文を読む スポンサード リンク
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