Quantum star-graph analogues of PT -symmetric square wells: Part II, spectra

For the non-Hermitian equilateral q-pointed star-shaped quantum graphs of our previous paper (Can. J. Phys. 90, 1287 (2012) doi:10.1139/p2012-107 ) we show that because of certain dynamical aspects of the model as controlled by the external, rotation-symmetric complex Robin boundary conditions, the spectrum is obtainable in a closed asymptotic-expansion form, in principle at least. Explicit formulae up to the second order are derived for illustration, and a few comments on their consequences are added.

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