Hermitian - non-Hermitian interfaces in quantum theory

TL;DR

This paper explores the conditions under which Hermitian and non-Hermitian quantum systems can overlap, showing that weakly nonlocal interactions can create interfaces between these two descriptions, challenging the traditional separation.

Contribution

It demonstrates that weakly nonlocal potentials can lead to overlaps between Hermitian and non-Hermitian quantum descriptions, which was previously thought to be impossible.

Findings

Overlaps between Hermitian and non-Hermitian systems can occur with weakly nonlocal interactions.

Analytically solvable models illustrate the emergence of interfaces.

The separation of the two families of operators is not always strict.

Abstract

In the global framework of quantum theory the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies these two families seem to have an empty overlap. In this paper we demonstrate that it is not so. We are going to show that whenever the interaction potentials are chosen weakly nonlocal, the separation of the two families may disappear. The overlaps alias interfaces between the Hermitian and non-Hermitian descriptions of the unitarily evolving quantum system in question may become non-empty. This assertion will be illustrated via a few analytically solvable elementary models.