Understanding Partial PT symmetry as weighted composition conjugation in Reproducing Kernel Hilbert Space :An application to non-hermitian Bose-Hubbard type Hamiltonian in Fock space

TL;DR

This paper explores partial PT-symmetry as weighted composition conjugation within Reproducing Kernel Hilbert Spaces, applying it to analyze non-Hermitian Bose-Hubbard Hamiltonians and their symmetry-breaking behaviors.

Contribution

It introduces a novel interpretation of partial PT-symmetry as weighted composition conjugation in RKHS and applies this framework to non-Hermitian Bose-Hubbard models.

Findings

Partial PT-symmetry is characterized as weighted composition conjugation.

The framework is applied to non-Hermitian Bose-Hubbard Hamiltonians.

Symmetry breaking phenomena are analyzed within this setting.

Abstract

A new kind of symmetry behaviour introduced as partialPT-symmetry is investigated in a typical Fock space setting understood as a Reproducing Kernel Hilbert Space (RKHS). The same kind of symmetry is understood for a nonhermitian Bose-Hubbard type Hamiltonian involving two boson operators as well as its eigenstates. The phenomenon of symmetry breaking has also been considered