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Cryptohermitian Hamiltonians on graphs. II. Hermitizations

Non-hermitian quantum graphs possessing real (i.e., in principle, observable) spectra are studied via their discretization. The discretized Hamiltonians are assigned, constructively, an elementary pseudometric and/or a more complicated metric. Both these constructions make the Hamiltonian Hermitian, respectively, in an auxiliary (Krein or Pontryagin) vector space or in a less friendly (but more useful) Hilbert space of quantum mechanics.

preprint2011arXivOpen access
Miloslav Znojil
math-phmath.MPquant-ph
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Miloslav Znojil

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