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Cited by 102Cold Atom Physics and Bose-Einstein CondensatesStrong Light-Matter InteractionsQuantum, superfluid, helium dynamics

Bose-Einstein Condensates in Atomic Gases: Simple Theoretical Results

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Castin, Y.·2007·Les Houches - Ecole d’Ete de Physique Theorique
DOI 10.1007/3-540-45338-5_1
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  • In low-dimensional geometries, a general condition for mean-field validity is that the characteristic kinetic energy exceeds the interaction energy, ε_kin ≫ ε_int, equivalently n ξ^d ≫ 1.

    “a quite general formulation involves the characteristic kinetic and interaction energies, ε kin = ħ 2 n 2/d /2m ≫ ε int = g nl n or, equivalently, the number of particles per healing length, nξ d ≫ 1”

    From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [74]

    Section 9.2 (p. 132–133) gives a one-dimensional condition for the Born approximation and relates it to a large particle number in the condensate, lending some support to a weak-interaction criterion for mean-field treatment. The copy does not state the claimed general low-dimensional criterion ε_kin ≫ ε_int or its equivalence to nξ^d ≫ 1. Section 5.3.4 (p. 60–61) defines the healing length, but applies it to a different validity condition for classical hydrodynamics. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • For three-dimensional dilute Bose-Einstein condensates, the mean-field approach is valid when the diluteness parameter n_3d a_sc^3 is much less than 1.

    “for three-dimensional gases, the condition can be expressed in terms of a diluteness condition n 3d a 3 sc ≪ 1, where n 3d is the three-dimensional density and a sc is the atom-atom collisional scattering length”

    From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [74]

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Cited by

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Authors
Castin, Y.
Affiliations
Laboratoire Kastler Brossel (FR)
Corresponding author
Castin, Y.
Venue
Les Houches - Ecole d’Ete de Physique Theorique
Publisher
Springer Berlin Heidelberg
Published
2007-07-02
Volume
72
Pages
1-136
DOI
10.1007/3-540-45338-5_1
OpenAlex
W1642381609
Cited by
102
References
0
Citations by year
2026: 2 · 2025: 3 · 2024: 3 · 2023: 4 · 2022: 7 · 2021: 9 · 2020: 3 · 2019: 4 · 2018: 6 · 2017: 7 · 2016: 4 · 2015: 5 · 2014: 3 · 2013: 5 · 2012: 3
FWCI
34.31
Type
book chapter
Language
en
Open access
Locations
  • Springer eBooks (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • HAL (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum, superfluid, helium dynamics
Keywords
Bose-Einstein condensate, ideal Bose gas, critical temperature, thermal de Broglie wavelength, Riemann zeta function, thermodynamic limit, phase transitions, non-interacting bosons, periodic boundary conditions

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