Behavior of Exceptional Point abundance at small loss

Determine how the number (or density) of S-matrix Exceptional Points of order 2 varies with uniform absorption strength η in the interval 0<η≤1 for generic non-Hermitian scattering systems, establishing whether it increases, remains stable, or monotonically decreases and quantifying the scaling behavior.

Background

The paper demonstrates that any nonzero loss splits a diabolic point into two Exceptional Points of opposite charge, implying EPs exist at infinitesimal loss. However, beyond this splitting, the dependence of EP abundance on small but finite loss is unclear.