Stability of solutions of the nonlinear Schrödinger equation for trapped Bose-condensed atoms with negative scattering lengths

Watanabe, Kimitaka; Mukai, Tetsuya; Mukai, Toshiharu

doi:10.1103/physreva.55.3639

Cited by 9 publications

(11 citation statements)

References 10 publications

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“…The latter value of N c,new agrees well with the one in the experiment, which is about 10 3[13]. It is also consistent with the theoretical ones obtained by different approaches, which are (1 ∼ 3) × 10 3 [31]-[40],[45]-[51].…”

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confidence: 90%

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Stability of Bose–einstein Condensates Confined in Traps

Tsurumi

Morise

Wadati

2000

Int. J. Mod. Phys. B

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Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by use of the variational method. The anlysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross-Pitaevskii equation which is known in nonlinear physics as the nonlinear Schrödinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.

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“…This problem has been discussed also in Refs. [79,45]. For g = −1, the energy (4.1.4) with the harmonic potential (4.1.2) is written as…”

Section: ) H ≤ 0 Casementioning

confidence: 99%

Stability of Bose–einstein Condensates Confined in Traps

Tsurumi

Morise

Wadati

2000

Int. J. Mod. Phys. B

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“…This is agreement with Pitaevskii's analysis of the system [24], where it is shown that an attractive interaction leads to collapse of the gas for energies more than ω below the ideal gas ground state energy. Similar conclusions are drawn in [25]. The results of the many-body calculation are compared to the mean field approximation (Gross-Pitaevskii), which is approached as the particle number increases.…”

Section: A Ground State Energymentioning

confidence: 53%

Exact diagonalization of the Hamiltonian for trapped interacting bosons in lower dimensions

Haugset

Haugerud

1998

Phys. Rev. A

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We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the ground state energy and density profile. We discuss the dependence of these quantities on both interaction strength g and particle number N . The ground state properties are compared to the predictions of the Gross-Pitaevskii equation, and the agreement is surprisingly good even for relatively low particle numbers. We also calculate the specific heat based on the obtained energy spectra.

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“…By combining Eqs. (16) and (17) we get the following second-order differential equation for the evolution of the widtḧ…”

Section: Variational Approach and Governing Equationsmentioning

confidence: 99%

“…Due to the diluteness of BEC, most theoretical works on collective excitations are mainly focused on considering the two-body interaction by means of the Gross-Pitaevskii equation (GPE) [6,7,8,9]. A long side with the experimental progress with BECs in atomic waveguides and on the surface of atomic chips, which involve a strong compression of the traps, a significant increase of the density of BECs can be achieved; thus, three-body interaction may also play an important role in the process of collective excitations [10,11,12,13], and stability of trapped BEC [14,15,16]. Specially, it is reported in Ref.…”

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confidence: 99%

Stability of logarithmic Bose–Einstein condensate in harmonic trap

Bouharia

2015

Mod. Phys. Lett. B

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In this paper we investigate the stability of a recently introduced Bose-Einstein condensate (BEC) which involves logarithmic interaction between atoms. The Gaussian variational approach is employed to derive equations of motion for condensate widths in the presence of a harmonic trap. Then we derive the analytical solutions for these equations and find them to be in good agrement with numerical data. By analyzing deeply the frequencies of collective oscillations, and the mean-square radius, we find that the system is always stable for both negative and positive week logarithmic coupling. However, for strong interaction the situation is quite different: our condensate collapses for positive coupling and oscillates with fixed frequency for negative one. These special results remain the most characteristic features of the logarithmic BEC compared to that involving two-body and three-body interactions.

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Stability of solutions of the nonlinear Schrödinger equation for trapped Bose-condensed atoms with negative scattering lengths

Cited by 9 publications

References 10 publications

Stability of Bose–einstein Condensates Confined in Traps

Stability of Bose–einstein Condensates Confined in Traps

Exact diagonalization of the Hamiltonian for trapped interacting bosons in lower dimensions

Stability of logarithmic Bose–Einstein condensate in harmonic trap

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