--- _id: '154' abstract: - lang: eng text: We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for m∈[m2,m2−1]. So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). article_number: '19' article_processing_charge: No article_type: original author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. 2018;21(3). doi:10.1007/s11040-018-9275-3 apa: Moser, T., & Seiringer, R. (2018). Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-018-9275-3 chicago: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System with Point Interactions.” Mathematical Physics Analysis and Geometry. Springer, 2018. https://doi.org/10.1007/s11040-018-9275-3. ieee: T. Moser and R. Seiringer, “Stability of the 2+2 fermionic system with point interactions,” Mathematical Physics Analysis and Geometry, vol. 21, no. 3. Springer, 2018. ista: Moser T, Seiringer R. 2018. Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. 21(3), 19. mla: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System with Point Interactions.” Mathematical Physics Analysis and Geometry, vol. 21, no. 3, 19, Springer, 2018, doi:10.1007/s11040-018-9275-3. short: T. Moser, R. Seiringer, Mathematical Physics Analysis and Geometry 21 (2018). date_created: 2018-12-11T11:44:55Z date_published: 2018-09-01T00:00:00Z date_updated: 2023-09-19T09:31:15Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s11040-018-9275-3 ec_funded: 1 external_id: isi: - '000439639700001' file: - access_level: open_access checksum: 411c4db5700d7297c9cd8ebc5dd29091 content_type: application/pdf creator: dernst date_created: 2018-12-17T16:49:02Z date_updated: 2020-07-14T12:45:01Z file_id: '5729' file_name: 2018_MathPhysics_Moser.pdf file_size: 496973 relation: main_file file_date_updated: 2020-07-14T12:45:01Z has_accepted_license: '1' intvolume: ' 21' isi: 1 issue: '3' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '09' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Mathematical Physics Analysis and Geometry publication_identifier: eissn: - '15729656' issn: - '13850172' publication_status: published publisher: Springer publist_id: '7767' quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Stability of the 2+2 fermionic system with point interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 21 year: '2018' ... --- _id: '1079' abstract: - lang: eng text: We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers. article_number: '6' article_processing_charge: No author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Hanne full_name: Van Den Bosch, Hanne last_name: Van Den Bosch citation: ama: Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 2017;20(2). doi:10.1007/s11040-017-9238-0 apa: Nam, P., & Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-017-9238-0 chicago: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry. Springer, 2017. https://doi.org/10.1007/s11040-017-9238-0. ieee: P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges,” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2. Springer, 2017. ista: Nam P, Van Den Bosch H. 2017. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 20(2), 6. mla: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2, 6, Springer, 2017, doi:10.1007/s11040-017-9238-0. short: P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20 (2017). date_created: 2018-12-11T11:50:02Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T11:53:35Z day: '01' department: - _id: RoSe doi: 10.1007/s11040-017-9238-0 external_id: isi: - '000401270000004' intvolume: ' 20' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1603.07368 month: '06' oa: 1 oa_version: Submitted Version project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Mathematical Physics, Analysis and Geometry publication_identifier: issn: - '13850172' publication_status: published publisher: Springer publist_id: '6300' quality_controlled: '1' scopus_import: '1' status: public title: Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 20 year: '2017' ...