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Scattering theory with localized non-Hermiticites, Phys

By Miloslav Znojil


For a non-Hermitian Hamiltonian with real spectrum one must introduce a nontrivial, ad hoc metric Θ = I in Hilbert space. H. F. Jones (Phys. Rev. D 76, 125003 (2007)) proposed and tested an extension of this strategy to the scattering from non-Hermitian localized interaction Hamiltonians. Using perturbation theory and an elementary example he choose a specific metric Θ (Mostafazadeh) = η and discovered that a strong non-locality in η makes the outgoing waves moving, paradoxically, in both directions. The resulting physical picture of the scattering required a thorough confirmation of its consistency, therefore. We show that the major part of the Jones’ paradox is caused by his specific choice of the metric. Nonperturbatively, via a few solvable models we demonstrate that and how the non-locality effects can be suppressed. In particular we recommend a replacement of the Jones ’ η by another, quasi-local metric Θ (QL) leading to the mere Hamiltonian-dependent renormalization of ingoing and outgoing waves in our models. 1

Year: 2013
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