Improved models for ideal Fermi gas and ideal Bose gas using quantum phase space
- URL: http://arxiv.org/abs/2407.09998v5
- Date: Sun, 19 Jan 2025 15:19:32 GMT
- Title: Improved models for ideal Fermi gas and ideal Bose gas using quantum phase space
- Authors: Rivo Herivola Manjakamanana Ravelonjato, Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Roland Raboanary, Naivo Rabesiranana, Solofoarisina Wilfrid Chrysante,
- Abstract summary: improved models leverage the concepts of quantum phase space and phase space representation of quantum mechanics.
Work provides a foundation for further applications in nanoscale systems, quantum gases, low-temperature physics, utra-cold physics and astrophysics.
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- Abstract: In this work, improvements are introduced into the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, directly linked to the uncertainty principle. These improved models leverage the recently developed concepts of quantum phase space and phase space representation of quantum mechanics. The Hamiltonian operator for a gas particle and its eigenstates are first determined, and quantum statistical mechanics is used to derive the thermodynamic properties of the ideal gas. Analytic expressions for thermodynamic quantities - including the grand canonical potential, particle number, internal energy, Von Neumann entropy, and pressure are derived, alongside the corresponding thermodynamic equations of state for both bosons and fermions. These corrections are particularly significant at low temperatures and in confined volumes, where quantum effects such as shape and size become prominent. The results also establish a direct link between thermodynamic functions and the quantum statistical variances of momenta. Importantly, the improved models recover well-known classical relations of the ideal gas in the high-temperature and large-volume limits, ensuring consistency with classical physics. By addressing quantum corrections and their thermodynamic implications, this work provides a foundation for further applications in nanoscale systems, quantum gases, low-temperature physics, utra-cold physics and astrophysics.
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