---
_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
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creator: dernst
date_created: 2019-04-09T07:45:38Z
date_updated: 2020-07-14T12:46:37Z
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date_created: 2019-04-09T07:45:38Z
date_updated: 2020-07-14T12:46:37Z
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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'
...