A physical interpretation for the non-Hermitian Hamiltonian

TL;DR

This paper establishes a connection between non-Hermitian and Hermitian Hamiltonians by showing their scattering states can be equivalent, providing a physical interpretation for non-Hermitian systems through solvable models.

Contribution

It introduces a method to relate non-Hermitian Hamiltonians to Hermitian ones via scattering states, regardless of PT symmetry breaking, supported by an exactly solvable model.

Findings

Scattering states of Hermitian and non-Hermitian lattices are equivalent.

Non-Hermitian Hamiltonians can be physically interpreted through their Hermitian counterparts.

The approach applies to both PT-symmetric and non-PT-symmetric cases.

Abstract

We explore a way of finding the link between a non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of Bethe Ansatz solutions for a class of non-Hermitian Hamiltonians and the scattering problems for the corresponding Hermitian Hamiltonians. It is shown that a scattering state of an arbitrary Hermitian lattice embedded in a chain as the scattering center shares the same wave function with the corresponding non-Hermitian tight binding lattice, which consists of the Hermitian lattice with two additional on-site complex potentials, no matter the non-Hermitian is broken PT symmetry or even non-PT. An exactly solvable model is presented to demonstrate the main points of this article.