  We investigate eigenvalue attraction for open quantum systems, biophysical
systems, and for Parity-Time symmetric materials. To determine whether an
eigenvalue and its complex conjugate of a real matrix attract, we derive
expressions for the second derivative of eigenvalues, which is dependent upon
contributions from inertial forces, attraction between an eigenvalue and its
complex conjugate, as well as the force of the remaining eigenvalues in the
spectrum.
