{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stability-of-the-one-electron-atom","title":"Stability of the one electron atom Schrödinger model with magnetic field in two dimensions","arxiv_id":"2310.12791","date":"2023-10-19","proceeding":null,"authors":["Ayoub Arraji","Saad Benjelloun","Salma Lahbabi"],"abstract":"We study the stability of the one electron atom Schr\\\"odinger model with self-generated magnetic field in two dimensions. The magnetic energy is taken of the general form $K\\int_{\\mathbb{R}^2} |B|^p$ and we study the stability of the model as a function of the power $p$ and the coupling constant $K$. We show that for $p>3/2$, the model is always stable, and for $p<3/2$, the model is always unstable. In the critical case $p=3/2$, there is a critical stability constant $K_c$, that we characterize in terms of zero modes of the Dirac-Weyl operator. The value of $K_c$ is approximated using analytic and numerical methods.","url_abs":"https://arxiv.org/abs/2310.12791v2","url_pdf":"https://arxiv.org/pdf/2310.12791v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"stability-of-the-one-electron-atom","repo_url":"https://github.com/sa3dben/zero_modes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}