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On a Relation among Bi-orthogonal system, Quadratic Non-Hermitian Boson operators with real spectrum and Partial PT symmetry in Fock Space (2206.01472v1)
Published 3 Jun 2022 in math-ph, math.MP, and quant-ph
Abstract: A new kind of symmetry called partial PT symmetry has been considered for non-hermitian quadratic boson operators obtained from a bi-orthogonal set of vectors in C2. The symmetry behaviour has been understood in Fock space considered as a Reproducing Kernel Hilbert Space(RKHS). The reality of eigenvalues and its connection to the possibility of the aforesaid symmetry (and symmetry breaking) are studied in terms of a deformation parameter responsible for nonhermiticity
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