PT-symmetric model with an 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 Schrödinger 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.

arXiv comment21 pages, 5 figures

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Cited by in corpus (4)

• Non-Hermitian Hamiltonians and similarity transformations
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity