Large amplitude spatial fluctuations in the boundary region of the Bose-Einstein condensate in the Gross-Pitaevskii regime

J. A. Tuszynski, J. Middleton, S. Portet, J. M. Dixon, Ole Bang, Peter Leth Christiansen, M. Salerno

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    The Gross-Pitaevskii regime of a Bose-Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross-Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas-Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations. (C) 2003 Elsevier Science B.V. All rights reserved.
    Original languageEnglish
    JournalPhysica A: Statistical Mechanics and its Applications
    Volume325
    Issue number3-4
    Pages (from-to)455-476
    ISSN0378-4371
    DOIs
    Publication statusPublished - 2003

    Cite this

    @article{edf9e44fdfca43988c26764f15c69c9f,
    title = "Large amplitude spatial fluctuations in the boundary region of the Bose-Einstein condensate in the Gross-Pitaevskii regime",
    abstract = "The Gross-Pitaevskii regime of a Bose-Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross-Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas-Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations. (C) 2003 Elsevier Science B.V. All rights reserved.",
    author = "Tuszynski, {J. A.} and J. Middleton and S. Portet and Dixon, {J. M.} and Ole Bang and Christiansen, {Peter Leth} and M. Salerno",
    year = "2003",
    doi = "10.1016/S0378-4371(03)00287-5",
    language = "English",
    volume = "325",
    pages = "455--476",
    journal = "Physica A: Statistical Mechanics and its Applications",
    issn = "0378-4371",
    publisher = "Elsevier",
    number = "3-4",

    }

    Large amplitude spatial fluctuations in the boundary region of the Bose-Einstein condensate in the Gross-Pitaevskii regime. / Tuszynski, J. A.; Middleton, J.; Portet, S.; Dixon, J. M.; Bang, Ole; Christiansen, Peter Leth; Salerno, M.

    In: Physica A: Statistical Mechanics and its Applications, Vol. 325, No. 3-4, 2003, p. 455-476.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Large amplitude spatial fluctuations in the boundary region of the Bose-Einstein condensate in the Gross-Pitaevskii regime

    AU - Tuszynski, J. A.

    AU - Middleton, J.

    AU - Portet, S.

    AU - Dixon, J. M.

    AU - Bang, Ole

    AU - Christiansen, Peter Leth

    AU - Salerno, M.

    PY - 2003

    Y1 - 2003

    N2 - The Gross-Pitaevskii regime of a Bose-Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross-Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas-Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations. (C) 2003 Elsevier Science B.V. All rights reserved.

    AB - The Gross-Pitaevskii regime of a Bose-Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross-Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas-Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations. (C) 2003 Elsevier Science B.V. All rights reserved.

    U2 - 10.1016/S0378-4371(03)00287-5

    DO - 10.1016/S0378-4371(03)00287-5

    M3 - Journal article

    VL - 325

    SP - 455

    EP - 476

    JO - Physica A: Statistical Mechanics and its Applications

    JF - Physica A: Statistical Mechanics and its Applications

    SN - 0378-4371

    IS - 3-4

    ER -