Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

The Equilibrium Structure of Lithium Salt Solutions in Ether-Functionalized Ammonium Ionic Liquids

Molecular dynamics simulations have been performed for ionic liquids based on a ternary mixture of lithium and ammonium cations and a common anion, bis(trifluoromethylsulfonyl)imide, [Tf2N](-). We address structural changes resulting from adding Li+ in ionic liquids with increasing length of an ether-functionalized chain in the ammonium cation. The calculation of static structure factors reveals the lithium effect on charge ordering and intermediate range order in comparison with the neat ionic liquids. The charge ordering is modified in the lithium solution because the coordination of [Tf2N](-) toward Li+ is much stronger than ammonium cations. Intermediate range order is observed in neat ionic liquids based on ammonium cations with a long chain, but in the lithium solutions, there is also a nonhomogenous distribution of Li+ cations. The presence of Li+ enhances interactions between the ammonium cations due to correlations between the oxygen atom of the ether chain and the nitrogen atom of another ammonium cation.