Swanson Hamiltonian: non-PT-symmetry phase

TL;DR

This paper investigates the non-Hermitian Swanson Hamiltonian in the non-PT-symmetry phase, using Gel'fand triplet formalism to analyze its spectrum and physical interpretations, including exceptional points of infinite order.

Contribution

It introduces a formalism-based analysis of the Swanson Hamiltonian's non-PT phase, revealing its diverse physical system representations and spectral properties.

Findings

Different physical systems modeled by the Hamiltonian depending on parameters

Construction of generalized eigenfunctions using Gel'fand triplet formalism

Identification of exceptional points of infinite order

Abstract

In this work, we study the non-hermitian Swanson hamiltonian, particularly the non-PT symmetry phase. We use the formalism of Gel'fand triplet to construct the generalized eigenfunctions and the corresponding spectrum. Depending on the region of the parameter model space, we show that the Swanson hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. We also discussed the presence of Exceptional Points of infinite order.