Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality

@article{Nagao2020FamiliesOT,
title={Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality},
author={T. Nagao and G. Akemann and M. Kieburg and I. Parra},
journal={Journal of Physics A},
year={2020},
volume={53},
pages={075201}
}

We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse, due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature $\beta=2$ we can use the technique of planar orthogonal polynomials, borrowed from random matrix theory, to explicitly determine all $k$-point correlation functions for a fixed number of particles $N$. These are given by the determinant of the kernel of the corresponding orthogonal… CONTINUE READING