标题： N粒子费米二维系统在稀释 regime 下通过长程电和磁双体奇异势相互作用的 Hartree 动力学推导 显示英文标题

标题： Derivation of the Hartree dynamics for a N-particles fermionic 2D system interacting via long-range electric and magnetic two-body singular potentials in a dilute regime

摘要： 我们证明，当N很大时，一个由N个费米子组成的二维系统，通过成对的电和磁奇异相互作用，其初始数据为Slater形式，随着时间的推移保持其Slater结构。 换句话说，系统的波函数可以近似为一个Slater行列式，其轨道根据一组耦合的N个Chern-Simons- Schrödinger类型的有效方程演化。 该结果适用于稀疏区域，在该区域中，密度在与粒子数成比例的大体积上为一阶。 系统的成对磁特性意味着需要处理三体势的对角化，这是本文的主要数学创新。 显示英文摘要

摘要： We show that a 2-dimensional system of N fermions interacting through a pairwise electric and magnetic singular interactions with Slater initial data preserves its Slater structure over time when N gets large. In other words, the wave function of the system can be approximated by a Slater determinant whose orbitals evolves according to a coupled system of N Chern-Simons- Schr\"odinger type effective equations. The result holds in a dilute regime where the density is of order one on a large volume proportional to the number of particles. The pairwise magnetic feature of the system implies to deal with the diagonalization of three-body potentials which is the main mathematical innovation of the paper.