Titlebook: Non-Hermitian Hamiltonians in Quantum Physics; Selected Contributio Fabio Bagarello,Roberto Passante,Camillo Trapani Conference proceedings

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,Deformed and SUSY-Deformed Graphene: First Results,g .-pseudo bosons and the other supersymmetric quantum mechanics. In particular, in connection with .-pseudo bosons, we show how biorthogonal sets arise, and we discuss when these sets are bases for the Hilbert space where the model is defined, and when they are not. For the SUSY extension of the mo

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Localised Nonlinear Modes in the ,-Symmetric Double-Delta Well Gross-Pitaevskii Equation,the form of two .-function wells, where one well loses particles while the other one is fed with atoms at an equal rate. The parameters of the constructed solutions are expressible in terms of the roots of a system of two transcendental algebraic equations. We also furnish a simple analytical treatm

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The EMM and the Spectral Analysis of a Non Self-adjoint Hamiltonian on an Infinite Dimensional Hilbce. The presented operator has real eigenvalues and can be diagonalized when it is expressed in terms of pseudo-bosons, which do not behave as ordinary bosons under the adjoint transformation, but obey the Weil-Heisenberg commutation relations.

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Bessel Sequences, Riesz-Like Bases and Operators in Triplets of Hilbert Spaces,med in a previous paper. It is shown, in particular, that every .-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schr?dinger-type operators is considered. Moreover, some of the simplest operat

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Mathematical and Physical Meaning of the Crossings of Energy Levels in ,-Symmetric Systems,ses through one of its energy-crossing points . Kato’s exceptional points (EP), its physical interpretation may . change even when the crossing energies themselves do not complexify. The anomalous physical phase-transition mechanism of the change is revealed, attributed to the EP-related mathematics

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Physical Aspect of Exceptional Point in the Liouvillian Dynamics for a Quantum Lorentz Gas,s paper is the weakly-coupled one-dimensional quantum perfect Lorentz gas. The effective Liouvillian for the system derived by applying the Brillouin-Wigner-Feshbach formalism takes non-Hermitian form due to resonance singularity, thus its spectra take complex values. We find that the complex spectr