Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917041853693952 |
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| author | Aldunate, Danko González-Brantes, Juan Manuel Bosch, Hanne Van Den |
| author_facet | Aldunate, Danko González-Brantes, Juan Manuel Bosch, Hanne Van Den |
| contents | In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of potentials are considered. For bounded Hermitian potentials $V$ satisfying $|V(x)| \lesssim |x|^{-1}$ for large $|x|$, we recover the leading term, which may include a logarithmic correction if $V(x) \sim |x|^{-1}$ at infinity. For possibly non-Hermitian $L^1$ potentials satisfying a suitable moment condition, we obtain the second term in the asymptotic expansion. The first result is based on a min-max principle adapted to the non-relativistic limit, while the second result is obtained via the Birman-Schwinger principle and resolvent expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit Aldunate, Danko González-Brantes, Juan Manuel Bosch, Hanne Van Den Mathematical Physics Functional Analysis In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of potentials are considered. For bounded Hermitian potentials $V$ satisfying $|V(x)| \lesssim |x|^{-1}$ for large $|x|$, we recover the leading term, which may include a logarithmic correction if $V(x) \sim |x|^{-1}$ at infinity. For possibly non-Hermitian $L^1$ potentials satisfying a suitable moment condition, we obtain the second term in the asymptotic expansion. The first result is based on a min-max principle adapted to the non-relativistic limit, while the second result is obtained via the Birman-Schwinger principle and resolvent expansions. |
| title | Asymptotics for eigenvalues of one-dimensional Dirac operators in the weak coupling limit |
| topic | Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2510.21947 |