Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential

TL;DR

This paper investigates a non-Hermitian PT-symmetric extension of the $A_{N-1}$ Calogero model without confinement, demonstrating the absence of spectral singularities and analyzing scattering properties.

Contribution

It introduces a non-Hermitian PT-symmetric deformation of the Calogero model and shows that spectral singularities do not occur in this setup.

Findings

No spectral singularity exists in the model.

Transmission coefficient is zero for all energies.

Reflection coefficient is unity for all energies.

Abstract

We consider non-Hermitian PT-symmetric deformation of $A_{N-1}$ type Calogero model without confining potential to investigate the possible existence of spectral singularity. By considering the Wronskian between asymptotic incoming and outgoing scattering state wave functions, we found that there exist no spectral singularity in this model. We further explicitly show that the transmission coefficient vanishes and the reflection coefficient becomes unity for all values of the energy in such a momentum dependent non-Hermitian PT-symmetric model.