Physics counterpart of the PT non-hermitian tight-binding chain

TL;DR

This paper establishes a connection between PT non-Hermitian Hamiltonians and Hermitian Hamiltonians by linking PT eigenstates to resonance transmission states in extended Hermitian systems, offering a new perspective on their relationship.

Contribution

It introduces a novel method to relate PT non-Hermitian Hamiltonians to Hermitian systems via scattering and resonance transmission analysis.

Findings

PT eigenstates correspond to resonance transmission states in Hermitian systems.

Real-energy eigenstates of PT lattices share wave functions with Hermitian resonant states.

The approach provides a physical interpretation of PT symmetry in terms of scattering phenomena.

Abstract

We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any real-energy eigenstate of a PT tight-binding lattice with on-site imaginary potentials shares the same wave function with a resonant transmission state of the corresponding Hermitian lattice embedded in a chain. It indicates that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the resonance transmission state of the extended Hermitian Hamiltonian.