---
OA_place: repository
OA_type: green
_id: '7524'
abstract:
- lang: eng
  text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional
    Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$
    and inverse temperature $\\beta$ differs from the one of the non-interacting system
    by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$.
    Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ =
    \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless
    critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho
    \\ll 1$ and if $\\beta \\rho \\gtrsim 1$."
article_number: '1910.03372'
article_processing_charge: No
arxiv: 1
author:
- first_name: Andreas
  full_name: Deuchert, Andreas
  id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87
  last_name: Deuchert
  orcid: 0000-0003-3146-6746
- first_name: Simon
  full_name: Mayer, Simon
  id: 30C4630A-F248-11E8-B48F-1D18A9856A87
  last_name: Mayer
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
    Bose gas. I. Lower bound. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.1910.03372">10.48550/arXiv.1910.03372</a>
  apa: Deuchert, A., Mayer, S., &#38; Seiringer, R. (n.d.). The free energy of the
    two-dimensional dilute Bose gas. I. Lower bound. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.1910.03372">https://doi.org/10.48550/arXiv.1910.03372</a>
  chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy
    of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>ArXiv</i>, n.d. <a
    href="https://doi.org/10.48550/arXiv.1910.03372">https://doi.org/10.48550/arXiv.1910.03372</a>.
  ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional
    dilute Bose gas. I. Lower bound,” <i>arXiv</i>. .
  ista: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute
    Bose gas. I. Lower bound. arXiv, 1910.03372.
  mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose
    Gas. I. Lower Bound.” <i>ArXiv</i>, 1910.03372, doi:<a href="https://doi.org/10.48550/arXiv.1910.03372">10.48550/arXiv.1910.03372</a>.
  short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv (n.d.).
corr_author: '1'
date_created: 2020-02-26T08:46:40Z
date_published: 2019-10-08T00:00:00Z
date_updated: 2026-04-08T07:25:40Z
day: '08'
department:
- _id: RoSe
doi: 10.48550/arXiv.1910.03372
ec_funded: 1
external_id:
  arxiv:
  - '1910.03372'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.03372
month: '10'
oa: 1
oa_version: Preprint
page: '61'
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '7790'
    relation: later_version
    status: public
  - id: '7514'
    relation: dissertation_contains
    status: public
status: public
title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...