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

Authors

Alexandre Eremenko
Andrei Gabrielov

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.

Date of this Version

2010

Repository Citation

Eremenko, Alexandre and Gabrielov, Andrei, "Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families" (2010). Department of Earth, Atmospheric, and Planetary Sciences Faculty Publications. Paper 107.
https://docs.lib.purdue.edu/easpubs/107

Link Out to Full Text

http://arxiv.org/abs/1005.1696