Dispersion of first sound in a weakly interacting ultracold Fermi liquid
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909764313677824 |
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| author | Repplinger, Thomas Huang, Songtao Ji, Yunpeng Navon, Nir Kurkjian, Hadrien |
| author_facet | Repplinger, Thomas Huang, Songtao Ji, Yunpeng Navon, Nir Kurkjian, Hadrien |
| contents | At low temperature, a normal gas of unpaired spin-1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length $a$, the sole parameter of the short-range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, {as the uncontrolled error made by the relaxation time approximations increases when the temperature $T$ drops below the Fermi temperature}. Here, we study sound waves in the hydrodynamic regime up to second order in the Chapman-Enskog's expansion. We find that the frequency $ω_q$ of the sound wave is shifted above its linear departure as $ω_q=c_1 q(1+αq^2τ^2)$ where $c_1$ and $q$ are the speed and wavenumber of the sound wave and the typical collision time $τ$ scales as $1/a^2T^2$. Besides the shear viscosity, the coefficient $α$ is described by a single second-order collision time which we compute exactly from an analytical solution of the transport equation, resulting in a positive dispersion $α>0$. Our results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second-order hydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dispersion of first sound in a weakly interacting ultracold Fermi liquid Repplinger, Thomas Huang, Songtao Ji, Yunpeng Navon, Nir Kurkjian, Hadrien Quantum Gases Statistical Mechanics Atomic Physics At low temperature, a normal gas of unpaired spin-1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length $a$, the sole parameter of the short-range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, {as the uncontrolled error made by the relaxation time approximations increases when the temperature $T$ drops below the Fermi temperature}. Here, we study sound waves in the hydrodynamic regime up to second order in the Chapman-Enskog's expansion. We find that the frequency $ω_q$ of the sound wave is shifted above its linear departure as $ω_q=c_1 q(1+αq^2τ^2)$ where $c_1$ and $q$ are the speed and wavenumber of the sound wave and the typical collision time $τ$ scales as $1/a^2T^2$. Besides the shear viscosity, the coefficient $α$ is described by a single second-order collision time which we compute exactly from an analytical solution of the transport equation, resulting in a positive dispersion $α>0$. Our results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second-order hydrodynamics. |
| title | Dispersion of first sound in a weakly interacting ultracold Fermi liquid |
| topic | Quantum Gases Statistical Mechanics Atomic Physics |
| url | https://arxiv.org/abs/2409.10099 |