Related papers: Distribution Function for $n \ge g$ Quantum Particles

Distribution Function for $n \ge g$ Quantum Particles

URL: http://arxiv.org/abs/2411.09877v1
Date: Fri, 15 Nov 2024 01:53:48 GMT
Title: Distribution Function for $n \ge g$ Quantum Particles
Authors: Shimul Akhanjee,
Abstract summary: The anomalous behavior of $nI(varepsilon)$ precludes Bose-Einstein condensation (BEC) An exhaustive classification scheme is presented for both distinguishable and indistinguishable, particles and energy levels.
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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.

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