Admissible perturbations and false instabilities in PT-symmetric quantum systems

0489154 - ÚJF 2019 RIV US eng J - Journal Article
Znojil, Miloslav
Admissible perturbations and false instabilities in PT-symmetric quantum systems.
Physical Review A. Roč. 97, č. 3 (2018), č. článku 032114. ISSN 2469-9926. E-ISSN 2469-9934
R&D Projects: GA ČR GA16-22945S
Institutional support: RVO:61389005
Keywords : quantum theory * states * Hilbert spaces
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.907, year: 2018

One of the most characteristic mathematical features of the PT-symmetric quantum mechanics is the explicit Hamiltonian dependence of its physical Hilbert space of states H = H(H). Some of the most important physical consequences are discussed, with emphasis on the dynamical regime in which the system is close to phase transition. Consistent perturbation treatment of such a regime is proposed. An illustrative application of the innovated perturbation theory to a non-Hermitian but PT-symmetric user-friendly family of J-parametric 'discrete anharmonic' quantum Hamiltonians H = H((lambda) over right arrow) is provided. The models are shown to admit the standard probabilistic interpretation if and only if the parameters remain compatible with the reality of the spectrum, (lambda) over right arrow is an element of D-(physical). In contradiction to conventional wisdom, the systems are then shown to be stable with respect to admissible perturbations, inside the domain D-(physical), even in the immediate vicinity of the phase-transition boundaries partial derivative D-(physical).
Permanent Link: http://hdl.handle.net/11104/0283625