Spectral singularity and non-Hermitian<i>PT</i>-symmetric extension of an<i>A</i>_{<i>N</i>− 1}-type Calogero model without confining potential

Abstract

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