论文标题
几个旋转$ 1/2 $相互作用的费米子的静态和动态属性被困在谐波电位上
Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
论文作者
论文摘要
我们提供了一些相互作用的自旋$ 1/2 $费米子的特性的详细研究，被困在一维谐波振荡器电位中。假定该相互作用是由接触三角电势很好地表示。通过直接对角线化技术获得的数值结果与非相互作用和强烈相互作用方案的分析表达式结合使用。 $ n = 2 $ case用于用问题的已知精确解决方案对我们的数值技术进行基准测试。在以教程的方式详细描述了数值方法后，我们以$ n = 2、3、4 $和5粒子的形式介绍了系统的静态特性，例如低能频谱，一体密度矩阵，地下密度。然后，我们使用动态结构函数和相应的总和，然后突然淬灭相互作用强度的系统，首先考虑系统的动态特性，首先探索呼吸模式的激发。
We provide a detailed study of the properties of a few interacting spin $1/2$ fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The $N=2$ case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for $N=2, 3, 4$ and 5 particles, e.g. low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.
