Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation

• URL: http://arxiv.org/abs/2204.13350v1
• Date: Thu, 28 Apr 2022 08:43:18 GMT
• Title: Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation
• Authors: E. Cavalcanti, N.M. Alvarenga, F. Reis, J.R. Mahon, C.A. Linhares, J.A. Louren\c{c}o
• Abstract summary: We study the transition from $mathcalPT$-unbroken to $mathcalPT$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum. We also discuss the influence of the boundary condition and the model parameters in the exceptional line that marks the $\mathcal{PT}$ breaking.

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