Pseudo-Hermitian systems, involutive symmetries and pseudofermions

TL;DR

This paper explores the structure of multilevel pseudo-Hermitian systems with specific symmetries, demonstrating their representation via pseudofermionic operators and analyzing a detailed four-level Hamiltonian example.

Contribution

It introduces a framework for representing certain pseudo-Hermitian systems with involutive symmetries using pseudofermionic operators, extending previous understanding.

Findings

Representation of 2N-level Hamiltonians with pseudofermionic operators

Explicit analysis of a four-level Hamiltonian with odd time-reversal symmetry

Extension of SO(5) Hermitian Hamiltonian to pseudo-Hermitian case

Abstract

We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy can be represented in the oscillator-like form in terms of pseudofermionic creation and annihilation operators for both real and complex eigenvalues. The example of most general four-level traceless Hamiltonian with odd time-reversal symmetry, which is an extension of the SO(5) Hermitian Hamiltonian, is considered in greater and explicit detail.