We develop a non-Hermitian effective theory for a repulsively interacting Fermi gas in the excited branch. The on-shell $T$-matrix is employed as a complex-valued interaction term, which describes a repulsive interaction between atoms in the excited branch and a two-body inelastic decay to the attractive branch. To see the feature of this model, we have addressed, in the weak coupling regime, the excitation properties of a repulsive Fermi polaron as well as the time-dependent number density. The analytic expressions obtained for these quantities qualitatively show a good agreement with recent experiments. By calculating the dynamical transverse spin susceptibility in the random phase approximation, we show that a ferromagnetic system with nonzero polarization undergoes a dynamical instability and tends towards a heterogeneous phase.

中文翻译：

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超冷费米气体中的非厄米铁磁性

我们为激发分支中相互排斥的费米气体开发了一个非厄米有效理论。壳上 $T$ 矩阵被用作复值相互作用项，它描述了激发分支中原子之间的排斥相互作用和吸引分支的双体非弹性衰变。为了查看该模型的特征，我们在弱耦合状态下解决了排斥费米极化子的激发特性以及与时间相关的数密度。为这些量获得的解析表达式定性地表明与最近的实验非常吻合。通过计算随机相位近似中的动态横向自旋磁化率，我们表明具有非零极化的铁磁系统会经历动态不稳定性并趋向于异相。