Distribution Function for n ≥ g Quantum Particles

2024/11/15 by Shimul Akhanjee, Akhanjee, Shimul
Decision Sciences · Mathematics · #Probability and Risk Models #Mathematical Approximation and Integration #Advanced Mathematical Theories

paper · pdf · doi:10.48550/arxiv.2411.09877

Abstract

A new quantum mechanical distribution function n^I(ε), is derived for the condition n ≥ g, where in contrast to the exclusion principle n ≤ g for fermions, each energy state must be populated by at least one particle. Although the particles share many features with bosons, the anomalous behavior of n^I(ε) precludes Bose-Einstein condensation (BEC) due to the required occupancy of the excited states, which creates a permanently pressurized background at T=0, similar to the degeneracy pressure of fermions. An exhaustive classification scheme is presented for both distinguishable and indistinguishable, particles and energy levels based on Richard Stanley's twelvefold way in combinatorics.

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