Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 163

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Flat bands, Dirac cones, and atom dynamics in an optical lattice

Open access
Apaja, V., Hyrkäs, M., Manninen, M.·2010·Physical Review A
DOI 10.1103/physreva.82.041402
Open this paper in CoChat — free account

Abstract

We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight-binding or Hubbard models. In the case of fermions the release of the harmonic confinement removes fast atoms occupying the Dirac cones while those occupying the flat band remain immobile. Using exact diagonalization and dynamics we demonstrate that a similar strong occupation of the flat band does not happen in the bosonic case and furthermore that the mean-field model is not capable of describing the dynamics of the boson cloud.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physreva.82.041402

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 2 references

Research works printed but not linked: 26

  1. 10.1038/nphys138 · DOI · Paper page
  2. A. C. Leggett, 2006, Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed Matter Systems, 10.1093/acprof:oso/9780198526438.001.0001 · DOI · Paper page
  3. C. J. Pethick, 2008, Bose-Einstein Condensation in Dilute Gases, 10.1017/CBO9780511802850 · DOI · Paper page
  4. 10.1103/RevModPhys.80.885 · DOI · Paper page
  5. 10.1103/PhysRevLett.105.013902 · DOI
  6. 10.1103/PhysRevLett.93.030601 · DOI · Paper page
  7. 10.1103/PhysRevA.72.053612 · DOI
  8. 10.1103/PhysRevLett.99.070401 · DOI · Paper page
  9. 10.1103/PhysRevLett.103.080406 · DOI
  10. 10.1143/PTP.6.306 · DOI
  11. 10.1103/PhysRevB.45.12377 · DOI · Paper page
  12. 10.1039/b003682j · DOI · Paper page
  13. 10.1103/PhysRevB.65.081307 · DOI
  14. 10.1103/PhysRevB.81.014421 · DOI
  15. 10.1140/epjb/e2008-00113-2 · DOI
  16. 10.1016/S0022-4596(03)00239-1 · doi:10.1016/s0022-4596(03)00239-1
  17. 10.1143/JPSJ.74.1918 · doi:10.1143/jpsj.74.1918
  18. 10.1103/RevModPhys.81.109 · DOI · Paper page
  19. 10.1038/nature08942 · DOI · Paper page
  20. 10.1103/PhysRevB.54.R17296 · DOI
  21. 10.1103/PhysRevB.81.041410 · DOI · Paper page
  22. N. Ashcroft, 1976, Solid State Physics
  23. 10.1088/1751-8113/42/27/275302 · doi:10.1088/1751-8113/42/27/275302
  24. 10.1007/BF02731494 · DOI · Paper page
  25. L. P. Pitaevskii, 1961, Zh. Eksp. Teor. Fiz., 40, 646
  26. L. P. Pitaevskii, 1961, Sov. Phys. JETP, 13, 451

Cited by

See all 163

Metadata

Authors
Apaja, V., Hyrkäs, M., & Manninen, M.
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2010-10-13
Volume
82
Issue
4
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.82.041402
OpenAlex
W1969037018
Cited by
163
References
2
FWCI
3.10
Type
journal article
Language
en
Open access
bronze
Licence
link.aps.org/licenses/aps-default-license (vor)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Flat bands, Dirac cones, and atom dynamics in an optical lattice. https://app.cochat.ai/papers/10.1103/physreva.82.041402
The paper
Apaja, V., Hyrkäs, M., & Manninen, M. (2010). Flat bands, Dirac cones, and atom dynamics in an optical lattice. Physical Review A. https://doi.org/10.1103/physreva.82.041402

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.