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arXiv · 1005.1696

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

Alexandre Eremenko·Andrei Gabrielov
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Abstract

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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Alexandre Eremenko, Andrei Gabrielov. 2010-08-23. Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families. https://arxiv.org/abs/1005.1696

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