Bose-Einstein-condensed gases with arbitrary strong interactions

Yukalov, V. I.; Yukalova, E. P.

doi:10.1103/physreva.74.063623

Cited by 37 publications

(120 citation statements)

References 42 publications

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“…However, the importance of the anomalous average near the ground state has been stressed by some authors [18,19,20] who devised new variations of the HFB approximation in order to include that average.…”

Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

“…This way, the gap disappears. In the representative statistical ensemble approach [20,21], it is argued that the number of condensate particles N 0 deserves a special treatment because it appears as a new macroscopic quantity in the system. As a result, a new chemical potential µ 0 associated to N 0 should be introduced.…”

Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

“…The solution is now implicit, and Eqs. (17,18,19,20,21,26,27) have to be solved self-consistently. While it retains the elegance of the Bogoliubov approximation, and is supposedly applicable to more strongly-interacting cases, the HFB approximation suffers from a notorious problem related to the existence of a gap in the excitation spectrum [17], which is forbidden in the superfluid regime according to the Hugenholtz-Pines theorem [39].…”

Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

“…Several authors have suggested an improved HFB approximation by introducing that correlation by hand so that a gapless excitation spectrum is preserved [18,19]. More recently, Yukalov et al [20,21] proposed a treatment of the HFB approximation in the context of representative statistical ensembles which preserves both the correlation and absence of a gap, and aims at describing the strongly-interacting regime.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Danshita

Naidon²

2009

Phys. Rev. A

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We determine the ground-state properties of a gas of interacting bosonic atoms in a one-dimensional optical lattice. The system is modelled by the Bose-Hubbard Hamiltonian. We show how to apply the time-evolving block decimation method to systems with periodic boundary conditions, and employ it as a reference to find the ground state of the Bose-Hubbard model. Results are compared with recently proposed approximate methods, such as Hartree-Fock-Bogoliubov (HFB) theories generalised for strong interactions and the variational BijlDingle-Jastrow method. We find that all HFB methods do not bring any improvement to the Bogoliubov theory and therefore provide correct results only in the weakly-interacting limit, where the system is deeply in the superfluid regime. On the other hand, the variational Bijl-Dingle-Jastrow method is applicable for much stronger interactions, but is essentially limited to the superfluid regime as it reproduces the superfluid-Mott insulator transition only qualitatively.

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Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

Section: Extended Bogoliubov Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Danshita

Naidon²

2009

Phys. Rev. A

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“…Here, the notation ... stands for the ensemble average over all possible disorder configurations [28]. The effect of disorder in a lattice can be characterized by two important parameters: the concentration of disorder κ = n imp /n and the ratio of effective interaction strength…”

Section: Macroscopic Dynamics Of a Bec In The Presence Of Weak DImentioning

confidence: 99%

Collective excitations of a trapped Bose-Einstein condensate in the presence of weak disorder and a two-dimensional optical lattice

Liang

2010

Phys. Rev. A

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We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D dimensional crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.

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Bose-Einstein condensation and gauge symmetry breaking

Yukalov

2007

Laser Phys. Lett.

134

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The fundamental problem is analized, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement that, though gauge symmetry breaking helps for describing Bose-Einstein condensation, but the latter, in principle, does not require any symmetry breaking. This, however, is not correct. The analysis is based on the known mathematical theorems. But in order not to overcomplicate the presentation and to make it accessible to all readers, technical details are often omitted here. The emphasis is made on the following basic general facts: Spontaneous breaking of gauge symmetry is the necessary and sufficient condition for Bose-Einstein condensation. Condensate fluctuations, in thermodynamic limit, are negligible. Their catastrophic behavior can arise only as a result of incorrect calculations, when a Bose-condensed system is described without gauge symmetry breaking. It is crucially important to employ the representative statistical ensembles equipped with all conditions that are necessary for a unique and mathematically correct description of the given statistical system. Only then one is able to develop a self-consistent theory, free of paradoxes.Comment: Latex file, 29 page

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Bose-Einstein-condensed gases with arbitrary strong interactions

Cited by 37 publications

References 42 publications

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Bose-Hubbard ground state: Extended Bogoliubov and variational methods compared with time-evolving block decimation

Collective excitations of a trapped Bose-Einstein condensate in the presence of weak disorder and a two-dimensional optical lattice

Bose-Einstein condensation and gauge symmetry breaking

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