| Autor: |
How, Pye Ton, Yip, S. -K. |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Phys. Rev. A 97, 063623 (2018) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevA.97.063623 |
| Popis: |
We consider the thermodynamic potential of a dilute Fermi gas with a contact interaction, at both finite temperature $T$ and non-zero effective magnetic fields $\mathbf{H}$, and derive the equation of state analytically using second order perturbation theory. Special attention is paid to the non-analytic dependence of $\Omega$ on temperature $T$ and (effective) magnetic field $\mathbf{H}$, which exhibits a crossover behavior as the ratio of the two is continuously varied. This non-analyticity is due to the particle-hole pair excitation being always gapless and long-ranged. The non-analytic crossover found in this paper can therefore be understood as an analog of the Ginzberg-Landau critical scaling, albeit only at the sub-leading order. We extend our results to an $\mathcal{N}_c$- component Fermi gas with an $\mathrm{SU}(\mathcal{N}_c)$-symmetric interaction, and point out possible enhancement of the crossover behavior by a large $\mathcal{N}_c$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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