Bose-Einstein distribution

The Bose-Einstein distribution tells you how many particles have a certain energy.

This last distribution is known as the Bose-Einstein distribution.

The particles obey the Bose-Einstein distribution and all occupy the ground state:

Here is the Bose-Einstein distribution function.

This result applies for each single-particle level and thus forms the Bose-Einstein distribution for the entire state of the system.

Viewed as a pure probability distribution, the Bose-Einstein distribution has found application in other fields:

The Bose-Einstein distribution, which applies only to a quantum system of non-interacting bosons, is easily derived from the grand canonical ensemble.

The Bose-Einstein distribution which describes bosons leads to Bose-Einstein condensation.

Multiplying by the phonon population (Bose-Einstein distribution, N) gives the total deformation potential, (the reason for the root will be apparent below).

In contrast with the Poisson distribution for a coherent light source, the Bose-Einstein distribution has characteristic of thermal light.

Thermal radiation has a Bose-Einstein distribution on very short time scales, and a normal distribution on longer timescales due to the central limit theorem.

Planck's law arises as a limit of the Bose-Einstein distribution, the energy distribution describing non-interactive bosons in thermodynamic equilibrium.

The Maxwell-Boltzmann distribution follows from this Bose-Einstein distribution for temperatures well above absolute zero, implying that .

(Fermions take their name from the Fermi-Dirac statistical distribution that they obey, and bosons from their Bose-Einstein distribution).

In the case of massless bosons such as photons and gluons, the chemical potential is zero and the Bose-Einstein distribution reduces to the Planck distribution.

In each case the value gives the thermodynamic average number of particles on the orbital: the Fermi-Dirac distribution for fermions, and the Bose-Einstein distribution for bosons.

Fermions such as electrons follow a Fermi-Dirac distribution and bosons such as phonons and photons follow a Bose-Einstein distribution.

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.

However near absolute zero, the Maxwell-Boltzmann distribution fails to account for the observed behaviour of the gas, and the (modern) Fermi-Dirac or Bose-Einstein distributions have to be used instead.

As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose-Einstein distribution, the Fermi-Dirac distribution and the Maxwell-Boltzmann distribution.

An ideal gas of bosons (e.g. a photon gas) will be governed by Bose-Einstein statistics and the distribution of energy will be in the form of a Bose-Einstein distribution.

He has also contributed conscientiously in the spin-off of technology from the space program, with applications in such diverse subjects as Bose-Einstein distribution in mathematical physics, symbolic and algebraic computation, computational physics and biomedical research.

This term cannot be found as easily or generally as the others - it is a statistical term representing the particle collisions, and requires knowledge of the statistics the particles obey, like the Maxwell-Boltzmann, Fermi-Dirac or Bose-Einstein distributions.

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.