Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach

TL;DR

This paper explores non-Hermitian Hamiltonians with real and complex eigenvalues using an sl(2,C) algebraic approach, extending potential algebras to analyze spectral transitions.

Contribution

It introduces an extension of potential algebras from Hermitian to non-Hermitian Hamiltonians via complex Lie algebra sl(2,C), providing a new framework for spectral analysis.

Findings

Extended potential algebras to non-Hermitian Hamiltonians

Provided an algebraic method to study real-to-complex eigenvalue transitions

Applied sl(2,C) approach to specific non-Hermitian systems

Abstract

Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A$_1$.