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Understanding Partial \(\mathcal {P}\mathcal {T}\) Symmetry as Weighted Composition Conjugation in Reproducing Kernel Hilbert Space: An application to Non-hermitian Bose-Hubbard Type Hamiltonian in Fock space

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Abstract

A new kind of symmetry behaviour introduced as partial \(\mathcal {P}\mathcal {T}\)-symmetry(henceforth \(\partial _{\mathcal {P}\mathcal {T}}\)) is investigated in a typical Fock space setting. The said Fock space is understood as a Reproducing Kernel Hilbert Space (RKHS). The same kind of symmetry is analysed for a non-hermitian Bose-Hubbard type Hamiltonian (involving two boson operators) along with its eigenstates. The phenomenon of symmetry breaking has also been considered.

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  1. Heritage Institute of Technology, Chowbaga Rd, Anandapur, Mundapara, Kolkata, 700107, India

    Arindam Chakraborty

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  1. Arindam Chakraborty
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Correspondence to Arindam Chakraborty.

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Chakraborty, A. Understanding Partial \(\mathcal {P}\mathcal {T}\) Symmetry as Weighted Composition Conjugation in Reproducing Kernel Hilbert Space: An application to Non-hermitian Bose-Hubbard Type Hamiltonian in Fock space. Int J Theor Phys 60, 3689–3697 (2021). https://doi.org/10.1007/s10773-021-04946-2

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  • DOI: https://doi.org/10.1007/s10773-021-04946-2

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