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A much simpler way to think of Bose–Einstein distribution function is to consider that n particles are denoted by identical balls and g shells are marked by g-1 line partitions. It is clear that the permutations of these n balls and g − 1 partitions will give different ways of arranging bosons in different energy levels.
The same team demonstrated in 2017 the first creation of a Bose–Einstein condensate in space [70] and it is also the subject of two upcoming experiments on the International Space Station. [71] [72] Researchers in the new field of atomtronics use the properties of Bose–Einstein condensates in the emerging quantum technology of matter-wave ...
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 .
In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral.
The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble.The grand potential for a Bose gas is given by: = = (). where each term in the sum corresponds to a particular single-particle energy level ε i; g i is the number of states with energy ε i; z is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical ...
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states as a differential, and summations over states as integrals.
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In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely ...