--- _id: '52' abstract: - lang: eng text: In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser citation: ama: Moser T. Point interactions in systems of fermions. 2018. doi:10.15479/AT:ISTA:th_1043 apa: Moser, T. (2018). Point interactions in systems of fermions. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1043 chicago: Moser, Thomas. “Point Interactions in Systems of Fermions.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1043. ieee: T. Moser, “Point interactions in systems of fermions,” Institute of Science and Technology Austria, 2018. ista: Moser T. 2018. Point interactions in systems of fermions. Institute of Science and Technology Austria. mla: Moser, Thomas. Point Interactions in Systems of Fermions. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1043. short: T. Moser, Point Interactions in Systems of Fermions, Institute of Science and Technology Austria, 2018. date_created: 2018-12-11T11:44:22Z date_published: 2018-09-04T00:00:00Z date_updated: 2023-09-27T12:34:14Z day: '04' ddc: - '515' - '530' - '519' degree_awarded: PhD department: - _id: RoSe doi: 10.15479/AT:ISTA:th_1043 file: - access_level: open_access checksum: fbd8c747d148b468a21213b7cf175225 content_type: application/pdf creator: dernst date_created: 2019-04-09T07:45:38Z date_updated: 2020-07-14T12:46:37Z file_id: '6256' file_name: 2018_Thesis_Moser.pdf file_size: 851164 relation: main_file - access_level: closed checksum: c28e16ecfc1126d3ce324ec96493c01e content_type: application/zip creator: dernst date_created: 2019-04-09T07:45:38Z date_updated: 2020-07-14T12:46:37Z file_id: '6257' file_name: 2018_Thesis_Moser_Source.zip file_size: 1531516 relation: source_file file_date_updated: 2020-07-14T12:46:37Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '115' 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_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '8002' pubrep_id: '1043' related_material: record: - id: '5856' relation: part_of_dissertation status: public - id: '154' relation: part_of_dissertation status: public - id: '1198' relation: part_of_dissertation status: public - id: '741' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Point interactions in systems of fermions type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ...