Non-Hermitian scattering on a tight-binding lattice

TL;DR

This paper investigates the scattering behavior and spectral properties of a quantum particle on a tight-binding lattice with a non-Hermitian imaginary potential, revealing exceptional points and spectral pairing phenomena.

Contribution

It provides a detailed analysis of non-Hermitian scattering dynamics, identifying exceptional points and spectral pairing in a tight-binding lattice with imaginary potentials.

Findings

Identification of an exceptional point at a specific potential strength

Spectral pairing with coalescing eigenstates at the exceptional point

At high potential strength, absorption decreases and mimics real potential effects

Abstract

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary potential is similar to that of a real potential. We quantify this similarity by utilizing properties of a localized eigenstate.