Distribution Function for $n \ge g$ Quantum Particles

TL;DR

This paper introduces a novel quantum distribution function for particles with occupancy constraints different from traditional fermions and bosons, revealing unique behaviors that prevent Bose-Einstein condensation.

Contribution

It derives a new distribution function for particles with minimum occupancy constraints and classifies particle-energy level systems using combinatorial methods.

Findings

The distribution function prevents Bose-Einstein condensation.

Particles exhibit fermion-like degeneracy pressure despite sharing features with bosons.

A comprehensive classification scheme for particle systems is developed.

Abstract

A new quantum mechanical distribution function $n^I(\varepsilon)$, is derived for the condition $n \ge g$, where in contrast to the exclusion principle $n \le g$ 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 $n^I(\varepsilon)$ 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.