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arXiv · 1711.05654

Spectral stability of bi-frequency solitary waves in Soler and Dirac--Klein--Gordon models

Nabile Boussaid·Andrew Comech
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Abstract

We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction (the Soler model) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and qudit states in the theory of quantum computing. We show the relation of $\pm 2\omega\mathrm{i}$ eigenvalues of the linearization at a solitary wave, Bogoliubov $\mathbf{SU}(1,1)$ symmetry, and the existence of bi-frequency solitary waves. We show that the spectral stability of these waves reduces to spectral stability of usual (one-frequency) solitary waves.

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Nabile Boussaid, Andrew Comech. 2017-11-15. Spectral stability of bi-frequency solitary waves in Soler and Dirac--Klein--Gordon models. https://arxiv.org/abs/1711.05654

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