Bose-Einstein distribution bosons

One of the simplest procedures to get the expression for the Fermi-Dirac (F-D) and the Bose-Einstein (B-E) distributions, is to apply the grand canonical ensemble methodology for a system of noninteracting indistinguishable particles, that is, fermions for the Fermi-Dirac distribution and bosons for the Bose-Einstein distribution. For these systems, the grand canonical partition function can be expressed as follows [12] ... 

At very low energy, many amorphous materials show a Boson peak , so-called because the temperature dependence of its intensity roughly scales with the Bose-Einstein distribution. Amorphous silica is no exception and has a peak at 40 cm. The origin of this has been controversial but in silica it appears to be related to either transverse acoustic modes or torsions of the Si04 tetrahedra with respect to one another [15]. 

Bose-Einstein distribution - A modification of the Boltzmann distribution which applies to a system of particles that are bosons. The number of particles of energy E is proportional to [e<, where g is a normalization constant, k is the... 

The Bose-Einstein Distribution Indistinguishable particles (such as particles with spin S = 0 or S = 1 and multiples thereof) without limiting the number that can occupy any state of energy e,. Such entities are called bosons. 

If the atoms in the gas have an integer spin, that is, if they are bosonic atoms, they are distributed among the quantum states in accordance with the Bose-Einstein distribution... 

This difference between fermions and bosons is reflected in how they occupy a set of states, especially as a function of temperature. Consider the system shown in Figure E.10. At zero temperature (T = 0), the bosons will try to occupy the lowest energy state (a Bose-Einstein condensate) while for the fermions the occupancy will be one per quantum state. At high temperatures the distributions are similar and approach the Maxwell Boltzman distribution. 

COVALENT BONDING involves a pair of electrons with opposite electron spin. The bond (or electron charge distribution) is essentially localized between nearest neighbor atoms that contribute electrons for the bonding. Since these electron pairs follow Bose-Einstein statistics, therefore they are known as boson. In this case the paired particles do not obey the Pauli Exclusion Principle and many electron pairs in the system may occupy the same energy level. 

An interesting phenomenon predicted for boson systems where the number of particles is fixed is that of Bose-Einstein condensation. This implies that, as the temperature is gradually reduced, there is a sudden occupation of the zero momentum state by a macroscopic number of particles. The number of particles per increment range of energy is sketched in Fig. 3 for temperatures above and just below the Bose-Einstein condensation temperature Tb. The distribution retains, at least approximately, the classical Maxwellian form until Tb is reached. Below Tj, there are two classes of particles those in the condensate (represented by the spike at = 0) and those in excited states. The criterion for a high or low temperature in a boson system is simply that of whether T >T or T < 7b, where 7b is given by ... 

---