---
_id: '6840'
abstract:
- lang: eng
  text: "We discuss thermodynamic properties of harmonically trapped\r\nimperfect
    quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition
    of the mean-field interparticle potential energy as compared\r\nto the homogeneous
    case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number
    of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and
    a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments
    that this model corresponds to the limiting case of\r\na long-ranged interparticle
    potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation
    similar to the well-known Kac scaling\r\nprocedure, which is presented here in
    a form adapted to the case of an isotropic\r\nharmonic trap. We show that within
    the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein
    condensation provided d > 1.\r\nThe main result of our analysis is that in d =
    1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically
    equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters
    aF and aB fulfill\r\nthe relation aB + aF = \x1F. This result supplements similar
    recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform
    imperfect\r\nrepulsive Bose and attractive Fermi gases."
article_number: '063101'
article_processing_charge: No
arxiv: 1
author:
- first_name: Krzysztof
  full_name: Mysliwy, Krzysztof
  id: 316457FC-F248-11E8-B48F-1D18A9856A87
  last_name: Mysliwy
- first_name: Marek
  full_name: Napiórkowski, Marek
  last_name: Napiórkowski
citation:
  ama: 'Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum
    gases in harmonic traps. <i>Journal of Statistical Mechanics: Theory and Experiment</i>.
    2019;2019(6). doi:<a href="https://doi.org/10.1088/1742-5468/ab190d">10.1088/1742-5468/ab190d</a>'
  apa: 'Mysliwy, K., &#38; Napiórkowski, M. (2019). Thermodynamics of inhomogeneous
    imperfect quantum gases in harmonic traps. <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/ab190d">https://doi.org/10.1088/1742-5468/ab190d</a>'
  chicago: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
    Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>. IOP Publishing, 2019. <a href="https://doi.org/10.1088/1742-5468/ab190d">https://doi.org/10.1088/1742-5468/ab190d</a>.'
  ieee: 'K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect
    quantum gases in harmonic traps,” <i>Journal of Statistical Mechanics: Theory
    and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019.'
  ista: 'Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect
    quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and
    Experiment. 2019(6), 063101.'
  mla: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous
    Imperfect Quantum Gases in Harmonic Traps.” <i>Journal of Statistical Mechanics:
    Theory and Experiment</i>, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:<a
    href="https://doi.org/10.1088/1742-5468/ab190d">10.1088/1742-5468/ab190d</a>.'
  short: 'K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and
    Experiment 2019 (2019).'
date_created: 2019-09-01T22:00:59Z
date_published: 2019-06-13T00:00:00Z
date_updated: 2023-08-29T07:19:13Z
day: '13'
department:
- _id: RoSe
doi: 10.1088/1742-5468/ab190d
ec_funded: 1
external_id:
  arxiv:
  - '1810.02209'
  isi:
  - '000471650100001'
intvolume: '      2019'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1810.02209
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
  eissn:
  - 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 2019
year: '2019'
...