On the Quantum Statistical Distributions Describing Finite Fermions and Bosons Systems

Abstract

A century old methodology for deriving statistical distribution using approximate Stirling’s formulation of the factorial becomes questionable. By avoiding the use of exaggerated approximations, a new picture of the energy distribution of fermions and bosons are presented. Energy distribution among fermions (or bosons) in systems with finite degeneracy are found to be degeneracy dependent. The presented point of view explains, successfully, presence of degeneracy pressure in ultra-cooled Fermi gas and predicts the minimum accessible temperature for finite degeneracy fermions system

Approximate processing of the level–level interference in an R-matrix formalism

“…In the R-matrix formalism, the configuration space formed in response to the reaction or interaction of a neutron with a target nucleus is the space of all possible degree-of-freedoms for nucleons in the system which is related to the existence of fermions (single nucleons) and bosons (paired nucleons) in the finite size of the nucleus [42]. The whole configuration space is divided into 'internal' and 'external' parts with a surface region, in physical space, defined by a channel radius a c , see figure 1.…”

Boltzmann or Gibbs Entropy? <br/>Thermostatistics of Two Models with Few Particles

“…From (7a) and (7b), and using (4b) and (5b) the temperature and specific heat can be obtained exactly, that is, without applying the Stirling's formula since it has be noticed that this approximation should be avoided for finite systems [15]- [17]. The results are shown in Figure 1 for N = 10, and in Figure 2 for N = 100.…”