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Stability boundaries of a Mathieu equation having PT symmetry

Quantum Physics 2019-09-04 v2 Mathematical Physics math.MP

Abstract

I have applied multiple-scale perturbation theory to a generalized complex PTPT-symmetric Mathieu equation in order to find the stability boundaries between bounded and unbounded solutions. The analysis suggests that the non-Hermitian parameter present in the equation can be used to control the shape and curvature of these boundaries. Although this was suggested earlier by several authors, analytic formulas for the boundary curves were not given. This paper is a first attempt to fill this gap in the theory.

Keywords

Cite

@article{arxiv.1812.04699,
  title  = {Stability boundaries of a Mathieu equation having PT symmetry},
  author = {Paulo A. Brandão},
  journal= {arXiv preprint arXiv:1812.04699},
  year   = {2019}
}