发表机构
Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS（凝聚态物质理论物理实验室，索邦大学，法国国家科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究将新重整化方案应用于低温原子费米气体，通过恢复已知微扰结果对标理论，研究输运动力学及零声速修正，开发数值方法求解输运方程，用于研究密度和极化响应函数从无碰撞到流体动力学区域的转变。
AI 中文摘要
本文延续arXiv:2511.15938的研究，在该文中我们开发了一种新的重整化方案来构建费米液体的量子化理论。在此，我们将此形式体系应用于低温原子费米气体，其中短程相互作用由s波散射长度$a$完全参数化。我们通过恢复费米气体静态性质的已知微扰结果来对标重整化理论，如状态方程的李 - 黄 - 杨展开、动量分布的加利茨基展开以及临界温度的戈尔科夫 - 梅利克·巴尔胡达罗夫前置指数修正。接着转向输运动力学，展示了在包含$a$的二阶修正时零声速存在前置指数修正。最后，我们开发了一种有效的数值方法来精确求解输运方程，并应用于研究密度和极化响应函数中从无碰撞到流体动力学区域的转变。
英文摘要
This article follows up on arxiv:2511.15938, in which we developed an Hamiltonian renormalization scheme to construct a quantized theory of Fermi liquids. Here, we apply this formalism to a low-temperature atomic Fermi gas where the short-range interactions are fully parametrized by the s-wave scattering length $a$. We benchmark our renormalized theory by recovering known perturbative results on the static properties of the Fermi gas, such as the Lee-Huang-Yang expansion of the equation of state, the Galitskii expansion of the momentum distribution, and the Gor'kov-Melik Barkhudarov preexponential correction to the critical temperature. We then turn to the transport dynamics and demonstrate the presence of a preexponential correction to the speed of zero sound when including corrections of second order in $a$. Finally, we develop an efficient numerical method to solve the transport equation exactly, and we apply it to study the crossover from the collisionless to the hydrodynamic regime in the density and polarisation response functions.
Comments41 pages, 15 figures. Second part of "A low-energy effective Hamiltonian for Landau quasiparticle". First part: [arXiv:2511.15938]
