Gapless Hartree-Fock-Bogoliubov approximation for Bose gases

Yukalov, V. I.; Kleinert, H.

doi:10.1103/physreva.73.063612

Cited by 69 publications

(124 citation statements)

References 39 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…Despite explicitly accounting for pair anomalous averages, and providing a lower total energy for the system, this approach is problematic as its homogeneous limit leads to a gap in the energy spectrum at low momenta, which violates the Goldstone theorem [39]. This inconsistency can be avoided by neglecting the anomalous average altogether (or using other tricks [40][41][42][43][44]), as discussed by Griffin [32,45] and implemented numerically in Refs. [46,47].…”

Section: Methodsmentioning

confidence: 99%

A Dynamical Self-Consistent Finite-Temperature Kinetic Theory: The ZNG Scheme

et al. 2013

View full text Add to dashboard Cite

We review a self-consistent scheme for modelling trapped weakly-interacting quantum gases at temperatures where the condensate coexists with a significant thermal cloud. This method has been applied to atomic gases by Zaremba, Nikuni, and Griffin, and is often referred to as ZNG. It describes both mean-field-dominated and hydrodynamic regimes, except at very low temperatures or in the regime of large fluctuations. Condensate dynamics are described by a dissipative Gross-Pitaevskii equation (or the corresponding quantum hydrodynamic equation with a source term), while the non-condensate evolution is represented by a quantum Boltzmann equation, which additionally includes collisional processes which transfer atoms between these two subsystems. In the mean-field-dominated regime collisions are treated perturbatively and the full distribution function is needed to describe the thermal cloud, while in the hydrodynamic regime the system is parametrised in terms of a set of local variables. Applications to finite temperature induced damping of collective modes and vortices in the mean-field-dominated regime are presented.

show abstract

Section: Methodsmentioning

confidence: 99%

A Dynamical Self-Consistent Finite-Temperature Kinetic Theory: The ZNG Scheme

et al. 2013

View full text Add to dashboard Cite

show abstract

“…(39), can be simplified by means of the Hartree-FockBogolubov approximation, as in Refs. [24][25][26][27][28][29]. However, the interaction of the random potential with atoms, described by part (40), cannot be treated in the simple mean-field procedure, since…”

Section: Stochastic Mean-field Approximationmentioning

confidence: 99%

“…[29]. Here we do not add explicitly such a linear killer, since for a uniform system or for a system uniform on average, linear in ψ 1 (r) terms do not arise and condition (15) is automatically satisfied [24][25][26][27][28][29].…”

Section: Bose Systems In Random Potentialsmentioning

confidence: 99%

“…For example, the self-consistent mean-field approximation [24][25][26][27][28][29] describes well the uniform Bose systems with any strong atomic interactions. But the region of applicability of this approximation can be limited for Bose atoms in a lattice at zero temperature in the vicinity of the superfluid-insulator phase transition [30].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bose systems in spatially random or time-varying potentials

2009

Self Cite

View full text Add to dashboard Cite

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

show abstract

“…A gapeless modification was proposed in [23] for homogenous Bose-condensates. Analysis of transport properties of Bose-condensates in mesoscopic waveguides was given in [24].…”

Section: Introductionmentioning

confidence: 99%

Effective Hamiltonian and excitation spectrum of harmonically trapped bosons

Rovenchak

2016

Low Temperature Physics

View full text Add to dashboard Cite

An approach is proposed to obtain an effective Hamiltonian of a harmonically trapped Bose-system. Such a Hamiltonian is quadratic in the creation-annihilation operators and certain approximations allow to simplify higher (three and four operator) products to the required form. After the Hamiltonian diagonalization, the expression for the excitation spectrum is obtained containing in particular temperature-dependent corrections. Numerical calculations are made for a one-dimensional system. Some prospects towards the extension of the suggested approach to study binary bosonic mixtures are briefly discussed.

show abstract

Gapless Hartree-Fock-Bogoliubov approximation for Bose gases

Cited by 69 publications

References 39 publications

A Dynamical Self-Consistent Finite-Temperature Kinetic Theory: The ZNG Scheme

A Dynamical Self-Consistent Finite-Temperature Kinetic Theory: The ZNG Scheme

Bose systems in spatially random or time-varying potentials

Effective Hamiltonian and excitation spectrum of harmonically trapped bosons

Contact Info

Product

Resources

About