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

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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.