The ideal gas of Bosons and Fermions in Harmonic Traps in the framework of Extended Uncertainty Principle

TL;DR

This paper investigates how the Extended Uncertainty Principle (EUP) influences the thermodynamics of ideal Bose and Fermi gases in harmonic traps, revealing modest effects and bounding the EUP parameter through comparison with experimental data.

Contribution

It introduces the impact of the Extended Uncertainty Principle on trapped ideal quantum gases and provides bounds on the EUP parameter based on thermodynamic analysis.

Findings

EUP causes modest changes in thermodynamic quantities.

The EUP parameter is bounded as $eta \,\leq 0.36654\times 10^{7} m^{-2}$.

Comparison with experimental data constrains the EUP effects.

Abstract

This manuscript studies harmonically trapped ideal Bose and Fermi gas systems and their thermodynamics in the framework of the Extended Uncertainty Principle (EUP). In particular, we demonstrated how the ground and thermal particle ratios, condensate temperature, internal energy, specific heat, and equation of state functions change in the EUP formalism. Following a comprehensive analysis, we concluded that the effect of the EUP on ideal Bose and Fermi gas systems remains relatively modest compared to the effect of the Gravitational (Generalised) Uncertainty Principle. { By comparing the obtained results with experimental data, we found that the EUP parameter is bounded as $\alpha \leq 0.36654\times 10^{7}\text{ \ }m^{-2}$.}