PT-symmetric model with an interplay between kinematical and dynamical non-localities

TL;DR

This paper introduces a new family of finite-dimensional, non-Hermitian PT-symmetric quantum models with multi-parametric, non-local potentials, highlighting their exact solvability and the interplay between kinematical and dynamical non-localities.

Contribution

It presents a novel class of exactly solvable PT-symmetric models with non-local potentials and explores the structure of their Hermitizing metrics, including closed-form solutions.

Findings

Exact solvability of Schrödinger equation for the models

Explicit form of Hermitizing metrics for a subfamily

Demonstration of interplay between kinematical and dynamical non-localities

Abstract

A new family of non-Hermitian PT-symmetric quantum models is proposed in which the Hamiltonians $H=T+V$ are finite-dimensional and in which the dynamical-input potential $V$ is multi-parametric and non-local. The choice is supported by the exact solvability of Schr\"{o}dinger equation and by the well known fact that in PT-symmetric models a non-locality is already present due to the generic kinematical non-diagonality of the Hermitizing metrics $\Theta$. For a subfamily of our $H$s, also {\em all\,} of the eligible metrics $\Theta$ appear obtainable in closed form.