  There is a common belief in the condensed matter community that bulk
quantities become insensitive to the boundary condition in the infinite-volume
limit. Here we reconsider this statement in terms of recent arguments of
non-Hermitian skin effects, -strong dependence of spectra on boundary
conditions for the non-Hermitian Hamiltonians-, in the traditional Green's
function formalism. We find the criterion for quantities to be
sensitive/insensitive against the boundary condition in Hermitian
correlated/disordered systems, which is characterized by the residue theorem.
We also discuss the uncertainty of the quasiparticle energy under the skin
effects in terms of nonnormal pseudospectra, which can be tested via the sharp
optical absorption from the bulk-surface coupling. Our result indicates that
"pseudo quantum number" emerges as a consequence of large nonnormality.
