---
_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.
    <i>Mathematical Physics Analysis and Geometry</i>. 2018;21(3). doi:<a href="https://doi.org/10.1007/s11040-018-9275-3">10.1007/s11040-018-9275-3</a>
  apa: Moser, T., &#38; Seiringer, R. (2018). Stability of the 2+2 fermionic system
    with point interactions. <i>Mathematical Physics Analysis and Geometry</i>. Springer.
    <a href="https://doi.org/10.1007/s11040-018-9275-3">https://doi.org/10.1007/s11040-018-9275-3</a>
  chicago: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System
    with Point Interactions.” <i>Mathematical Physics Analysis and Geometry</i>. Springer,
    2018. <a href="https://doi.org/10.1007/s11040-018-9275-3">https://doi.org/10.1007/s11040-018-9275-3</a>.
  ieee: T. Moser and R. Seiringer, “Stability of the 2+2 fermionic system with point
    interactions,” <i>Mathematical Physics Analysis and Geometry</i>, 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.” <i>Mathematical Physics Analysis and Geometry</i>, vol.
    21, no. 3, 19, Springer, 2018, doi:<a href="https://doi.org/10.1007/s11040-018-9275-3">10.1007/s11040-018-9275-3</a>.
  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
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  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
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. <i>Mathematical Physics, Analysis and Geometry</i>.
    2017;20(2). doi:<a href="https://doi.org/10.1007/s11040-017-9238-0">10.1007/s11040-017-9238-0</a>
  apa: Nam, P., &#38; Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von
    Weizsäcker theory with small nuclear charges. <i>Mathematical Physics, Analysis
    and Geometry</i>. Springer. <a href="https://doi.org/10.1007/s11040-017-9238-0">https://doi.org/10.1007/s11040-017-9238-0</a>
  chicago: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von
    Weizsäcker Theory with Small Nuclear Charges.” <i>Mathematical Physics, Analysis
    and Geometry</i>. Springer, 2017. <a href="https://doi.org/10.1007/s11040-017-9238-0">https://doi.org/10.1007/s11040-017-9238-0</a>.
  ieee: P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker
    theory with small nuclear charges,” <i>Mathematical Physics, Analysis and Geometry</i>,
    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.” <i>Mathematical Physics, Analysis
    and Geometry</i>, vol. 20, no. 2, 6, Springer, 2017, doi:<a href="https://doi.org/10.1007/s11040-017-9238-0">10.1007/s11040-017-9238-0</a>.
  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'
...