CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C

TL;DR

This paper explores CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators, revealing new structures in PT and CPT-symmetric quantum mechanics with potential applications to non-Hermitian polynomial oscillators.

Contribution

It introduces a novel approach to nonlinear SUSY QM with differential charge-operators, demonstrating integrability and real spectra in CPT-symmetric non-Hermitian systems.

Findings

Differential-operator form of charge C leads to new SUSY structures.

Integrability of intertwining relations aligns with nonlinear SUSY algebra.

CPT-symmetric SUSY QM yields PT-asymmetric polynomial oscillators with real spectra.

Abstract

A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric.