Two-Dimensional One Component Plasma and Non-Hermitian Random Matrices

非厄米矩阵特征值的联合概率密度函数具有与二维库仑荷等离子体的玻尔兹曼因子2D-OCP相同的形式。这种统计力学流体模型已经出现在物理和数学的几个领域。事实上，电荷的对数排斥发生在超导体、超流体、旋转玻色-爱因斯坦凝聚体等系统中的涡旋和位错之间的相互作用中。2D-OCP与分数量子霍尔效应理论中的Laughlin试探波函数也有相似之处。该项目将探索随机矩阵理论和2D-OCP之间的联系，以深入了解库仑电荷的等离子体。

The joint probability density function of the eigenvalues of Non-Hermitian Matrices has the same form of the Boltzmann factor of a two-dimensional plasma of Coulomb charges, 2D-OCP. This statistical mechanics fluid model has appeared in several areas of physics and mathematics. Indeed, the logarithmic repulsion of the charges occurs as interaction between vortices and dislocations in systems such as superconductors, superfluids, rotating Bose-Einstein condensates. There is also an analogy between the 2D-OCP and the Laughlin trial wave function in the theory of fractional quantum Hall effect. The project will explore the connection between Random Matrix Theory and the 2D-OCP to gain insight into plasmas of Coulomb charges.