Distribution Function for $n\ge g$ Quantum Particles

Abstract

A new quantum mechanical distribution function $n^I(\epsilon )$, 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 $n^I(\epsilon )$ 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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