Pseudospectra in non-Hermitian quantum mechanics
  We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics. 
D. Krejcirik, P. Siegl, M. Tater and J. Viola
math.SP math-ph math.MP quant-ph