In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed. We then use the resummation technique with the ladder approximation to obtain compact expressions for both the energy and/or the on-shell self-energy in infinite spin-degenerated systems. Diagrammatic resummation technique has the advantage in general to be predictive in a region of density larger compared to many-body perturbation theory. It also leads to non-diverging limit as $|a_s| \rightarrow + \infty$. Still, the obtained expressions are rather complex functional of the Fermi momentum $k_F$. We introduce the full phase-space average or the partial phase-space methods respectively applied to the energy or to the self-energy to simplify their dependences in terms of $(a_s k_F)$ while keeping the correct limit at low density and the non-diverging property at large $|a_s k_F|$. Quasi-particle properties of Fermi system in various regime of density and scattering length are then illustrated. Our conclusion is that such simplified expressions where the direct link is made with the low energy constant without fine-tuning can provide a clear guidance to obtain density functional theory beyond the perturbative regime. However, quasi-particle properties close or near unitary cannot be reproduced unless this limit is explicitly used as a constraint. We finally discuss how such approximate treatment of quasi-particle can guide the development of density functional theory for strongly interacting Fermi systems.
Surface energy coefficient of a N2LO Skyrme energy functional : a semiclassical Extended Thomas-Fermi approach
我们推广到N2 LO Skyrme泛函的半经典方法的Grammaticos和Voros，以计算扩展的托马斯费米表达式的新的密度和电流出现在N2 LO水平。在一维对称半无限核物质模型中，利用简单的类费米密度分布，我们得到了一个简单易用的表面能计算公式，其中包括中心项、密度相关项和自旋轨道项，直到$\hbar^2$ .这样的公式可以很容易地被用来作为第一次尝试约束新的N2 LO Skyrme参数化的表面性质。本文中测试的N2 LO参数化示出表现出的移位（相比于一个完整的Hartree-Fock计算），这是定量类似于传统的Skyrme参数化得到的一个。
