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arXiv · 2511.17451

On gap properties for the linearized 1D Dirac--Soler model

Danko Aldunate·Julien Ricaud·Edgardo Stockmeyer
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Abstract

We study spectral properties of the Dirac operator $L_0$ arising as the upper-right off-diagonal block in the linearization around standing wave solutions of the one-dimensional Soler model with power nonlinearity $f(s)=s|s|^{p-1}$, $p>0$. Our main results concern the so-called gap property: we show that if $p \geq 1$, then the only eigenvalues of $L_0$ are its ground state energies, $-2\omega$ and $0$. In contrast, for $p<1$, additional eigenvalues appear from the thresholds of the essential spectrum. Furthermore, we prove that the thresholds never admit eigenvalues and that they have at most one resonance.

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Danko Aldunate, Julien Ricaud, Edgardo Stockmeyer. 2025-11-21. On gap properties for the linearized 1D Dirac--Soler model. https://arxiv.org/abs/2511.17451

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