Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States

TL;DR

This paper explores a new class of non-Hermitian su(2) Hamiltonians with real spectra, extending them into pseudo-Hermitian supersymmetric systems and constructing associated supercoherent states with bi-overcomplete properties.

Contribution

It introduces a pseudo-Hermitian supersymmetric extension of non-Hermitian su(2) Hamiltonians and develops a formalism for supercoherent states in these systems.

Findings

Established metrics for Hermitian equivalence of non-Hermitian Hamiltonians

Extended supercoherent states formalism to pseudo-Hermitian supersymmetric systems

Constructed bi-overcomplete supercoherent state families

Abstract

A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.