Non linear pseudo-bosons versus hidden Hermiticity

Abstract

The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear pseudo-bosons}. The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.

20 pp

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Cited by in corpus (10)

• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Hermitian dynamics in a class of pseudo-Hermitian networks
• More mathematics for pseudo-bosons
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
• Appearances of pseudo-bosons from Black-Scholes equation
• Damping and Pseudo-fermions
• Susy for non-Hermitian Hamiltonians, with a view to coherent states
• Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity