Finite accumulation point conjecture for transmission eigenvalues

Assume $k_\epsilon>1/\sqrt{2}$ and define

$$\kappa=\sqrt{k_\epsilon^2-\frac14}-\frac{i}{2}.$$

This number is a pole of the Drude–Lorentz term, and the transmission eigenvalues are discrete outside the compact region $K$ described in the paper. Finite accumulation point conjecture. The point $\kappa$ is a limit point of the transmission eigenvalues. Numerical evidence indicates that transmission eigenvalues accumulate at this pole, while the nature of this accumulation remains a completely open problem.