arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2409.10099cond-mat.quant-gascond-mat.stat-mechphysics.atom-ph
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弱相互作用超冷费米液体中第一声的色散

Dispersion of first sound in a weakly interacting ultracold Fermi liquid

Thomas Repplinger, Songtao Huang, Yunpeng Ji, Nir Navon, Hadrien Kurkjian

AI总结:

本文研究弱相互作用超冷费米液体中的第一声,通过Chapman-Enskog二阶展开和输运方程解析解精确得到正的声频色散系数。

摘要:

在低温下,由未配对自旋1/2费米子组成的正常气体是费米液体最纯净的实现之一。它由朗道理论描述,其中不需要唯象参数,因为准粒子相互作用函数可以按散射长度$a$的幂次进行微扰计算,而$a$是短程粒子间相互作用的唯一参数。然而,要获得输运方程的精确解,必须谨慎处理碰撞核,因为当温度$T$降至费米温度以下时,弛豫时间近似所带来的不受控误差会增大。在这里,我们研究流体动力学区域中的声波,直至Chapman-Enskog展开的二阶。我们发现声波频率$ω_q$相对于其线性起点发生上移,形式为$ω_q=c_1 q(1+αq^2τ^2)$,其中$c_1$和$q$分别是声波的速度和波数,而典型碰撞时间$τ$按$1/a^2T^2$缩放。除剪切黏度外,系数$α$由单个二阶碰撞时间描述;我们通过输运方程的解析解对其进行精确计算,得到正色散$α>0$。我们的结果表明,超冷原子费米气体是对二阶流体动力学进行定量检验的理想实验系统。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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