---
_id: '2338'
abstract:
- lang: eng
  text: Now that the low temperature properties of quantum-mechanical many-body systems
    (bosons) at low density, ρ, can be examined experimentally it is appropriate to
    revisit some of the formulas deduced by many authors 4-5 decades ago. For systems
    with repulsive (i.e. positive) interaction potentials the experimental low temperature
    state and the ground state are effectively synonymous -- and this fact is used
    in all modeling. In such cases, the leading term in the energy/particle is 2πℏ2aρ/m
    where a is the scattering length of the two-body potential. Owing to the delicate
    and peculiar nature of bosonic correlations (such as the strange N7/5 law for
    charged bosons), four decades of research failed to establish this plausible formula
    rigorously. The only previous lower bound for the energy was found by Dyson in
    1957, but it was 14 times too small. The correct asymptotic formula has recently
    been obtained by us and this work will be presented. The reason behind the mathematical
    difficulties will be emphasized. A different formula, postulated as late as 1971
    by Schick, holds in two-dimensions and this, too, will be shown to be correct.
    With the aid of the methodology developed to prove the lower bound for the homogeneous
    gas, two other problems have been successfully addressed. One is the proof by
    us that the Gross-Pitaevskii equation correctly describes the ground state in
    the `traps' actually used in the experiments. For this system it is also possible
    to prove complete Bose condensation, as we have shown. Another topic is a proof
    that Foldy's 1961 theory of a high density Bose gas of charged particles correctly
    describes its ground state energy.
alternative_title:
- Current Developments in Mathematics
article_processing_charge: No
arxiv: 1
author:
- first_name: Élliott
  full_name: Lieb, Élliott
  last_name: Lieb
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
- first_name: Jakob
  full_name: Yngvason, Jakob
  last_name: Yngvason
citation:
  ama: 'Lieb É, Solovej J, Seiringer R, Yngvason J. The ground state of the Bose gas.
    In: <i>Current Developments in Mathematics, 2001</i>. International Press; 2002:131-178.
    doi:<a href="https://doi.org/10.48550/arXiv.math-ph/0204027">10.48550/arXiv.math-ph/0204027</a>'
  apa: Lieb, É., Solovej, J., Seiringer, R., &#38; Yngvason, J. (2002). The ground
    state of the Bose gas. In <i>Current Developments in Mathematics, 2001</i> (pp.
    131–178). International Press. <a href="https://doi.org/10.48550/arXiv.math-ph/0204027">https://doi.org/10.48550/arXiv.math-ph/0204027</a>
  chicago: Lieb, Élliott, Jan Solovej, Robert Seiringer, and Jakob Yngvason. “The
    Ground State of the Bose Gas.” In <i>Current Developments in Mathematics, 2001</i>,
    131–78. International Press, 2002. <a href="https://doi.org/10.48550/arXiv.math-ph/0204027">https://doi.org/10.48550/arXiv.math-ph/0204027</a>.
  ieee: É. Lieb, J. Solovej, R. Seiringer, and J. Yngvason, “The ground state of the
    Bose gas,” in <i>Current Developments in Mathematics, 2001</i>, International
    Press, 2002, pp. 131–178.
  ista: 'Lieb É, Solovej J, Seiringer R, Yngvason J. 2002.The ground state of the
    Bose gas. In: Current Developments in Mathematics, 2001. Current Developments
    in Mathematics, , 131–178.'
  mla: Lieb, Élliott, et al. “The Ground State of the Bose Gas.” <i>Current Developments
    in Mathematics, 2001</i>, International Press, 2002, pp. 131–78, doi:<a href="https://doi.org/10.48550/arXiv.math-ph/0204027">10.48550/arXiv.math-ph/0204027</a>.
  short: É. Lieb, J. Solovej, R. Seiringer, J. Yngvason, in:, Current Developments
    in Mathematics, 2001, International Press, 2002, pp. 131–178.
date_created: 2018-12-11T11:57:04Z
date_published: 2002-01-01T00:00:00Z
date_updated: 2023-07-26T08:43:46Z
day: '01'
doi: 10.48550/arXiv.math-ph/0204027
extern: '1'
external_id:
  arxiv:
  - math-ph/0204027
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math-ph/0204027
month: '01'
oa: 1
oa_version: Published Version
page: 131 - 178
publication: Current Developments in Mathematics, 2001
publication_identifier:
  isbn:
  - '9781571461018'
publication_status: published
publisher: International Press
publist_id: '4588'
status: public
title: The ground state of the Bose gas
type: book_chapter
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '2002'
...