D. Krejcirik, P. Siegl, M. Tater, J. Viola

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.

http://arxiv.org/abs/1402.1082

Spectral Theory (math.SP); Mathematical Physics (math-ph); Quantum Physics (quant-ph)