Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families

Details Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families

2010-05-11

arxiv.org/abs/1005.1696v2

Moscow Math. J., 11, 3, (2011) 473-503

Physics

Mathematical Physics

The main result on singular perturbation is substantially improved, generalized, and the proof is simplified. 37 pages, 16 fig

Scientific paper

In the first part of the paper, we discuss eigenvalue problems of the form -w"+Pw=Ew with complex potential P and zero boundary conditions at infinity on two rays in the complex plane. We give sufficient conditions for continuity of the spectrum when the leading coefficient of P tends to 0. In the second part, we apply these results to the study of topology and geometry of the real spectral loci of PT-symmetric families with P of degree 3 and 4, and prove several related results on the location of zeros of their eigenfunctions.

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