The IR-truncated PT-symmetric V=ix3 model and its asymptotic spectral scaling graph


The IR-truncated PT-symmetric V=ix3 model and its asymptotic spectral scaling graph

Günther, U.; Stefani, F.

The PT-symmetric V=ix3 model over the real line is IR truncated and considered as Sturm-Liouville problem over a finite interval. Combining structures hidden in the Airy function setup of the V=ix model with WKB techniques developed by Bender and Jones in 2012 for the derivation of the real part of the spectrum of the ix3 model, a WKB and Stokes graph analysis for the complex spectral branches of the ix3 model as well as those of more general V=-(ix)2n+1 models over finite intervals is performed. Complementary insights into the spectra of these models are obtained by splitting the spectral branch-structure into purely real scale factors and asymptotic spectral scaling graphs. It turns out that the corresponding (structurally very simple) scaling graphs are geometrically invariant and cutoff-independent so that the infra-red (IR) limit can be formally taken. These graphs have invariantly existing PT phase transition regions. In this way, a simple heuristic picture and complementary explanation for the unboundedness of the C-operator and the lack of quasi-Hermiticity of the ix3 Hamiltonian over the real line is provided.

Keywords: PT-symmetric Quantum Mechanics; PT phase transition; spectral branch points; exceptional points; ix3 model; WKB techniques; IR truncation; C-operator; unboundedness; quasi-Hermiticity

  • Invited lecture (Conferences)
    Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII, 04.-13.06.2018, Bangalore, India

Permalink: https://www.hzdr.de/publications/Publ-28785
Publ.-Id: 28785