---
_id: '9769'
abstract:
- lang: eng
  text: A few years ago, flow equations were introduced as a technique for calculating
    the ground-state energies of cold Bose gases with and without impurities. In this
    paper, we extend this approach to compute observables other than the energy. As
    an example, we calculate the densities, and phase fluctuations of one-dimensional
    Bose gases with one and two impurities. For a single mobile impurity, we use flow
    equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation.
    We show that the mean-field approximation is accurate for all values of the boson-impurity
    interaction strength as long as the phase coherence length is much larger than
    the healing length of the condensate. For two static impurities, we calculate
    impurity-impurity interactions induced by the Bose gas. We find that leading order
    perturbation theory fails when boson-impurity interactions are stronger than boson-boson
    interactions. The mean-field approximation reproduces the flow equation results
    for all values of the boson-impurity interaction strength as long as boson-boson
    interactions are weak.
acknowledgement: We thank Matthias Heinz and Volker Karle for helpful comments on
  the manuscript; Zoran Ristivojevic for useful correspondence regarding mean-field
  calculations of induced impurity-impurity interactions; Fabian Grusdt for sharing
  with us the data for the densities presented in Ref. [14]. This work has received
  funding from the DFG Project No. 413495248 [VO 2437/1-1] (F. B., H.-W. H., A. G.
  V.) and European Union’s Horizon 2020 research and innovation programme under the
  Marie Skłodowska-Curie Grant Agreement No. 754411 (A. G. V.). M. L. acknowledges
  support by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON).
  H.-W.H. thanks the ECT* for hospitality during the workshop “Universal physics in
  Many-Body Quantum Systems – From Atoms to Quarks". This infrastructure is part of
  a project that has received funding from the European Union’s Horizon 2020 research
  and innovation programme under grant agreement No 824093. H.-W.H. was supported
  by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID
  279384907 - SFB 1245.
article_number: '008'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Fabian
  full_name: Brauneis, Fabian
  last_name: Brauneis
- first_name: Hans-Werner
  full_name: Hammer, Hans-Werner
  last_name: Hammer
- first_name: Mikhail
  full_name: Lemeshko, Mikhail
  id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
  last_name: Lemeshko
  orcid: 0000-0002-6990-7802
- first_name: Artem
  full_name: Volosniev, Artem
  id: 37D278BC-F248-11E8-B48F-1D18A9856A87
  last_name: Volosniev
  orcid: 0000-0003-0393-5525
citation:
  ama: 'Brauneis F, Hammer H-W, Lemeshko M, Volosniev A. Impurities in a one-dimensional
    Bose gas: The flow equation approach. <i>SciPost Physics</i>. 2021;11(1). doi:<a
    href="https://doi.org/10.21468/scipostphys.11.1.008">10.21468/scipostphys.11.1.008</a>'
  apa: 'Brauneis, F., Hammer, H.-W., Lemeshko, M., &#38; Volosniev, A. (2021). Impurities
    in a one-dimensional Bose gas: The flow equation approach. <i>SciPost Physics</i>.
    SciPost. <a href="https://doi.org/10.21468/scipostphys.11.1.008">https://doi.org/10.21468/scipostphys.11.1.008</a>'
  chicago: 'Brauneis, Fabian, Hans-Werner Hammer, Mikhail Lemeshko, and Artem Volosniev.
    “Impurities in a One-Dimensional Bose Gas: The Flow Equation Approach.” <i>SciPost
    Physics</i>. SciPost, 2021. <a href="https://doi.org/10.21468/scipostphys.11.1.008">https://doi.org/10.21468/scipostphys.11.1.008</a>.'
  ieee: 'F. Brauneis, H.-W. Hammer, M. Lemeshko, and A. Volosniev, “Impurities in
    a one-dimensional Bose gas: The flow equation approach,” <i>SciPost Physics</i>,
    vol. 11, no. 1. SciPost, 2021.'
  ista: 'Brauneis F, Hammer H-W, Lemeshko M, Volosniev A. 2021. Impurities in a one-dimensional
    Bose gas: The flow equation approach. SciPost Physics. 11(1), 008.'
  mla: 'Brauneis, Fabian, et al. “Impurities in a One-Dimensional Bose Gas: The Flow
    Equation Approach.” <i>SciPost Physics</i>, vol. 11, no. 1, 008, SciPost, 2021,
    doi:<a href="https://doi.org/10.21468/scipostphys.11.1.008">10.21468/scipostphys.11.1.008</a>.'
  short: F. Brauneis, H.-W. Hammer, M. Lemeshko, A. Volosniev, SciPost Physics 11
    (2021).
date_created: 2021-08-04T15:00:55Z
date_published: 2021-07-13T00:00:00Z
date_updated: 2023-08-11T10:25:44Z
day: '13'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.21468/scipostphys.11.1.008
ec_funded: 1
external_id:
  arxiv:
  - '2101.10958'
  isi:
  - '000680039500013'
file:
- access_level: open_access
  checksum: eaa847346b1a023d97bbb291779610ed
  content_type: application/pdf
  creator: asandaue
  date_created: 2021-08-10T11:44:59Z
  date_updated: 2021-08-10T11:44:59Z
  file_id: '9875'
  file_name: 2021_SciPostPhysics_Brauneis.pdf
  file_size: 1085300
  relation: main_file
  success: 1
file_date_updated: 2021-08-10T11:44:59Z
has_accepted_license: '1'
intvolume: '        11'
isi: 1
issue: '1'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '801770'
  name: 'Angulon: physics and applications of a new quasiparticle'
publication: SciPost Physics
publication_identifier:
  eissn:
  - 2542-4653
publication_status: published
publisher: SciPost
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Impurities in a one-dimensional Bose gas: The flow equation approach'
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 11
year: '2021'
...