Stability of Non-Hermitian Phases

Recent work on non-Hermitian physics in condensed matter systems has focused on the classification of new topological phases. The notion of a gap usually used to describe the stability of Hermitian phases is not sufficient in the presence of loss and gain terms. This work uses known results in the theory of psuedo-spectra and Jordan Normal Forms to detail the stability of novel non-Hermitian phases under different disorder profiles in 1D with some generalizations into higher dimensions. We find agreement with previous work in simple chiral models and single parameter disorder distributions of our generalized stability arguments.