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arXiv · 2204.13350

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

E. Cavalcanti·N. M. Alvarenga·F. Reis·J. R. Mahon·C. A. Linhares·J. A. Lourenço
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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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E. Cavalcanti, N. M. Alvarenga, F. Reis, J. R. Mahon, C. A. Linhares, J. A. Lourenço. 2022-04-28. Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation. https://arxiv.org/abs/2204.13350

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