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W4297041946 abstract "Two discrete N-level alternatives to the popular imaginary cubic oscillator are proposed and studied. In a certain domain ${cal D}$ of parameters $a$ and $z$ of the model, the spectrum of energies is shown real (i.e., potentially, observable) and the unitarity of the evolution is shown mediated by the construction of a (non-unique) physical, ad hoc Hilbert space endowed with a nontrivial, Hamiltonian-dependent inner-product metric $Theta$. Beyond ${cal D}$ the complex-energy curves are shown to form a Fibonacci-numbered geometric pattern and/or a topologically complete set of spectral loci. The dynamics-determining construction of the set of the eligible metrics is shown tractable by a combination of the computer-assisted algebra with the perturbation and extrapolation techniques. Confirming the expectation that for the local potentials the effect of the metric cannot be short-ranged." @default.
W4297041946 created "2022-09-26" @default.
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W4297041946 date "2012-03-01" @default.
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W4297041946 doi "https://doi.org/10.1016/j.aop.2011.12.009" @default.
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