Hermitian-Non-Hermitian Interfaces in Quantum Theory

0490005 - ÚJF 2019 RIV GB eng J - Journal Article
Znojil, Miloslav
Hermitian-Non-Hermitian Interfaces in Quantum Theory.
Advances in High Energy Physics. Roč. 2018, č. 4 (2018), č. článku 7906536. ISSN 1687-7357. E-ISSN 1687-7365
R&D Projects: GA ČR GA16-22945S
Institutional support: RVO:61389005
Keywords : quantum theory * Hermitian operators * non-Hermitian
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.953, year: 2018

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 will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlaps alias interfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.
Permanent Link: http://hdl.handle.net/11104/0284300