On gap properties for the linearized 1D Dirac--Soler model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912723198017536 |
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| author | Aldunate, Danko Ricaud, Julien Stockmeyer, Edgardo |
| author_facet | Aldunate, Danko Ricaud, Julien Stockmeyer, Edgardo |
| contents | 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, $-2ω$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On gap properties for the linearized 1D Dirac--Soler model Aldunate, Danko Ricaud, Julien Stockmeyer, Edgardo Mathematical Physics Analysis of PDEs Functional Analysis 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, $-2ω$ 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. |
| title | On gap properties for the linearized 1D Dirac--Soler model |
| topic | Mathematical Physics Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2511.17451 |