Pressure of a dilute spin-polarized Fermi gas: Lower bound
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912050664439808 |
|---|---|
| author | Lauritsen, Asbjørn Bækgaard Seiringer, Robert |
| author_facet | Lauritsen, Asbjørn Bækgaard Seiringer, Robert |
| contents | We consider a dilute spin-polarized Fermi gas at positive temperature in dimensions $d\in\{1,2,3\}$. We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^dρ^{2+2/d}$, where $a$ is the $p$-wave scattering length of the repulsive interaction and $ρ$ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01113 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pressure of a dilute spin-polarized Fermi gas: Lower bound Lauritsen, Asbjørn Bækgaard Seiringer, Robert Mathematical Physics We consider a dilute spin-polarized Fermi gas at positive temperature in dimensions $d\in\{1,2,3\}$. We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^dρ^{2+2/d}$, where $a$ is the $p$-wave scattering length of the repulsive interaction and $ρ$ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260). |
| title | Pressure of a dilute spin-polarized Fermi gas: Lower bound |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2307.01113 |