标题： 二维吸引性近玻色子任意子气体 显示英文标题

标题： 2D attractive almost-bosonic anyon gases

摘要： 在二维空间中，我们考虑一个由$N$任意子组成的系统，它们通过短程吸引的两体相互作用相互作用。 在稳定区域中，我们推导出平均场泡利泛函，作为多体量子力学的平均场极限。 此外，我们研究了坍缩区域中的坍缩现象，其中吸引力的强度趋于临界值（由立方 NLS 方程定义），同时考虑弱场区域，其中自生成磁场的强度趋于零。 显示英文摘要

摘要： In two-dimensional space, we consider a system of $N$ anyons interacts via a short range attractive two-body interaction. In the stable regime, we derive the average-field Pauli functional as the mean-field limit of many-body quantum mechanics. Furthermore, we investigate the collapse phenomenon in the collapse regime where the strength of attractions tends to a critical value (defined by the cubic NLS equation) while simultaneously considering the weak field regime where the strength of the self-generated magnetic field tends to zero.