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

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

arXiv comment9 pages

References in corpus (17)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• PT-Symmetric Quantum Mechanics
• PT-symmetric laser-absorber
• Visualization of Branch Points in PT-Symmetric Waveguides
• Biorthogonal Quantum Mechanics
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Observation of Fast Evolution in Parity-Time-Symmetric System
• Bifurcation diagram and pattern formation in superconducting wires with electric currents
• Coupled Oscillator Systems Having Partial PT Symmetry
• Flux-mediated optomechanics with a transmon qubit in the single-photon ultrastrong-coupling regime
• Tilted optical lattices with defects as realizations of PT symmetry in Bose-Einstein condensates
• Thermodynamics of Quantum Heat Bath
• Non-Hermitian Hamiltonians and similarity transformations
• Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field