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

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

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.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1941742 Studentship EP/N509619/1 18/09/2017 31/03/2021 Alex Little