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

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